TSTP Solution File: ALG397-1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ALG397-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 18:15:18 EDT 2024
% Result : Unsatisfiable 10.66s 3.35s
% Output : Refutation 11.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 745
% Syntax : Number of formulae : 1391 ( 317 unt; 100 typ; 0 def)
% Number of atoms : 3045 ( 774 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 17710 (1694 ~;1754 |; 0 &;14262 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 100 usr; 11 con; 0-5 aty)
% Number of variables : 2780 ( 0 ^2780 !; 0 ?;2780 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: $i > $i > $i > $o ).
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(v_q_____type,type,
v_q____: $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $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(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
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_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $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(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(class_Ring__and__Field_Opordered__ring_type,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Ring__and__Field_Omult__mono1_type,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(class_Ring__and__Field_Omult__mono_type,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_type,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_HOL_Ozero_type,type,
class_HOL_Ozero: $i > $o ).
thf(c_Polynomial_Ocoeff_type,type,
c_Polynomial_Ocoeff: $i > $i > $i ).
thf(c_Power_Opower_Opower_type,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $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_Oring__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_type,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: $i > $i > $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(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Ring__and__Field_Oring__1_type,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Polynomial_Opcompose_type,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
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_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Osemigroup__add_type,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_type,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(c_Polynomial_Opoly__rec_type,type,
c_Polynomial_Opoly__rec: $i > $i > $i > $i > $i > $i ).
thf(c_OrderedGroup_Ocomm__monoid__add__axioms_type,type,
c_OrderedGroup_Ocomm__monoid__add__axioms: $i > $i > $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_p_type,type,
v_p: $i ).
thf(c_HOL_OIf_type,type,
c_HOL_OIf: $i > $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i > $i > $i ).
thf(c_OrderedGroup_Omonoid__add__axioms_type,type,
c_OrderedGroup_Omonoid__add__axioms: $i > $i > $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $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_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(v_pa_____type,type,
v_pa____: $i ).
thf(v_c_____type,type,
v_c____: $i ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1_type,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1: $i > $i ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2_type,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2: $i > $i ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3_type,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3: $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1_type,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1: $i > $i > $i ).
thf(v_sko__unknown__thm__rrS__1_type,type,
v_sko__unknown__thm__rrS__1: $i > $i ).
thf(v_n_____type,type,
v_n____: $i ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2_type,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2: $i > $i ).
thf(131,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
thf(892,plain,
class_Ring__and__Field_Oordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Omonom @ B @ C @ A ) ) @ ( c_Polynomial_Omonom @ D @ C @ A ) )
= ( c_Polynomial_Omonom @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__monom_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Omonom @ B @ C @ A ) ) @ ( c_Polynomial_Omonom @ D @ C @ A ) )
= ( c_Polynomial_Omonom @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(1469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(62,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(760,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(614,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(2031,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(438,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(1633,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(275,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(1237,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) @ 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)],[275]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(1554,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(460,axiom,
class_Ring__and__Field_Oring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
thf(1686,plain,
class_Ring__and__Field_Oring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(1501,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(809,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(541,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(1879,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(1337,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(223,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1105,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(893,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)],[132]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ A @ C @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
thf(1840,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ A @ C @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ C ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Osmult @ B @ C @ A ) ) @ ( c_Polynomial_Osmult @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__right_0) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ C ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Osmult @ B @ C @ A ) ) @ ( c_Polynomial_Osmult @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(587,axiom,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
thf(1982,plain,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(12,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(666,plain,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
thf(1818,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).
thf(1855,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(486,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Suc @ B ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(1750,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Suc @ B ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(244,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
thf(1158,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(683,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(395,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(1522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
thf(994,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)],[178]) ).
thf(343,axiom,
! [A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__def_0) ).
thf(1401,plain,
! [A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ ( 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)],[343]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(477,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(1728,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(873,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)],[121]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(677,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( 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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(1596,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( 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)],[425]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_0) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(47,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(730,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(542,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(1882,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(52,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(741,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(580,axiom,
class_OrderedGroup_Osemigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add) ).
thf(1971,plain,
class_OrderedGroup_Osemigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(504,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(1793,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(861,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(468,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(1705,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(212,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
thf(1078,plain,
class_Ring__and__Field_Ocomm__ring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(1671,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(1608,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(616,axiom,
class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
thf(2035,plain,
class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(536,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(1867,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( 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)],[536]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(698,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)],[29]) ).
thf(14,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
thf(670,plain,
class_Ring__and__Field_Opordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= C )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= C )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(596,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
thf(1999,plain,
class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(82,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(797,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(558,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__commutes_0) ).
thf(1919,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_Opcompose @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pcompose_0) ).
thf(1988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_Opcompose @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(1761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(318,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(1342,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ 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)],[318]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
thf(930,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)],[149]) ).
thf(260,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
thf(1196,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)],[260]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Osmult @ B @ C @ A ) ) @ ( c_Polynomial_OpCons @ D @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__lemma_0) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Osmult @ B @ C @ A ) ) @ ( c_Polynomial_OpCons @ D @ 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)],[181]) ).
thf(622,axiom,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(2046,plain,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(499,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
thf(1782,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(359,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Opoly__rec @ B @ C @ ( c_Polynomial_OpCons @ D @ E @ A ) @ F @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ C @ D ) @ E ) @ ( c_HOL_OIf @ ( c_fequal @ E @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( tc_Polynomial_Opoly @ A ) ) @ B @ ( c_Polynomial_Opoly__rec @ B @ C @ E @ F @ A ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__rec_Osimps_0) ).
thf(1441,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Opoly__rec @ B @ C @ ( c_Polynomial_OpCons @ D @ E @ A ) @ F @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ C @ D ) @ E ) @ ( c_HOL_OIf @ ( c_fequal @ E @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( tc_Polynomial_Opoly @ A ) ) @ B @ ( c_Polynomial_Opoly__rec @ B @ C @ E @ F @ A ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ 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)],[35]) ).
thf(105,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
thf(841,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(168,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
thf(973,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)],[168]) ).
thf(634,axiom,
class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(2067,plain,
class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(484,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1746,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)],[484]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(898,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)],[135]) ).
thf(601,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(2010,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(1935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(376,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_Polynomial_Osmult @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
thf(1482,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_Polynomial_Osmult @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(1254,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(1628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(590,axiom,
( ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ v_c____ )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pc0_0) ).
thf(1985,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ v_c____ )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(618,axiom,
! [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ v_q____ @ tc_Complex_Ocomplex ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ v_c____ ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_q_I2_J_0) ).
thf(2039,plain,
! [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ v_q____ @ tc_Complex_Ocomplex ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ v_c____ ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(449,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1660,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(785,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)],[76]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(85,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(802,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(1279,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(593,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(1992,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(346,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1409,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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)],[43]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(917,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(31,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
thf(702,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(417,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
thf(1577,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)],[417]) ).
thf(365,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(1455,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(1832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(258,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
thf(1191,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)],[258]) ).
thf(368,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( c_OrderedGroup_Omonoid__add__axioms @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oaxioms_0) ).
thf(1462,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( c_OrderedGroup_Omonoid__add__axioms @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(1132,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(508,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
thf(1800,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)],[508]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0_0) ).
thf(1087,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)],[216]) ).
thf(375,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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(1479,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)],[375]) ).
thf(482,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/sandbox/benchmark/theBenchmark.p',cls_degree__0_0) ).
thf(1741,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)],[482]) ).
thf(227,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
thf(1115,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)],[227]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(1931,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Osmult @ B @ D @ A ) ) @ ( c_Polynomial_Osmult @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__left_0) ).
thf(1641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Osmult @ B @ D @ A ) ) @ ( c_Polynomial_Osmult @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(576,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(1963,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(559,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(1922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ 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)],[137]) ).
thf(546,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(1892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(309,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(1319,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(545,axiom,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
thf(1890,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)],[545]) ).
thf(166,axiom,
class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
thf(969,plain,
class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(320,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
thf(1347,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1013,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(770,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(514,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(1815,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(381,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(1494,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(569,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(1946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(611,axiom,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ v_q____ @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(2027,plain,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ v_q____ @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(331,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1373,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(1109,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(351,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/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1418,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)],[351]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(834,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(585,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(1978,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(242,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1151,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(189,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(1020,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_OpCons @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__pCons__0_0) ).
thf(1677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_OpCons @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 @ A @ B ) @ tc_Complex_Ocomplex ) @ C )
= ( hAPP @ ( c_Polynomial_Opoly @ B @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset_1) ).
thf(2073,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 @ A @ B ) @ tc_Complex_Ocomplex ) @ C )
= ( hAPP @ ( c_Polynomial_Opoly @ B @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(606,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(2017,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(1334,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(1,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ v_q____ @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(646,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ v_q____ @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(1858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(535,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(1864,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( 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)],[535]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset__poly_0) ).
thf(2058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(1377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(1215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(998,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(174,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(988,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(981,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(65,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(766,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(687,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(548,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(1896,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(877,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(26,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(692,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(361,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
thf(1447,plain,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__Suc_0) ).
thf(956,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(229,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 )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(1119,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 )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(70,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
thf(774,plain,
class_Ring__and__Field_Oordered__semidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(568,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(1943,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_1) ).
thf(1242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(110,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(849,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(446,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(1651,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(602,axiom,
class_HOL_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
thf(2011,plain,
class_HOL_Ozero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(920,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(80,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Opordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
thf(793,plain,
! [A: $i] :
( ( class_Ring__and__Field_Opordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(147,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(925,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(63,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(761,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Oorder @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_0) ).
thf(2047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Oorder @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(500,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(1783,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(644,axiom,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(2083,plain,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(358,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(1438,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(661,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)],[10]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(1768,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(714,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( 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)],[38]) ).
thf(630,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ B ) @ C ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__add_0) ).
thf(2061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ B ) @ C ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(597,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1 @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ A @ t_a ) @ t_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__decompose_1) ).
thf(2000,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1 @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ A @ t_a ) @ t_a @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ 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_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ 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_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(72,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(778,plain,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(394,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
!= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ ( c_Suc @ C ) ) )
| ( B = D )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(1519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
!= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ ( c_Suc @ C ) ) )
| ( B = D )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(1355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(231,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
thf(1123,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) ) @ ( 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)],[94]) ).
thf(451,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__0_0) ).
thf(1666,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(1370,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(550,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(1900,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(141,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(910,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(1174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ 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)],[251]) ).
thf(455,axiom,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(1676,plain,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(615,axiom,
( ( ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ v_c____ )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ ( v_sko__unknown__thm__rrS__1 @ v_pa____ ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_0) ).
thf(2032,plain,
( ( ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ v_c____ )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ ( v_sko__unknown__thm__rrS__1 @ v_pa____ ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(91,axiom,
class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
thf(815,plain,
class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(571,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(1951,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(635,axiom,
! [A: $i] : ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ v_c____ ) @ tc_Complex_Ocomplex ) @ ( c_RealVector_Onorm__class_Onorm @ ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ A ) @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_c_0) ).
thf(2068,plain,
! [A: $i] : ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ v_c____ ) @ tc_Complex_Ocomplex ) @ ( c_RealVector_Onorm__class_Onorm @ ( hAPP @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ A ) @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(830,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)],[98]) ).
thf(245,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
thf(1159,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)],[245]) ).
thf(502,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/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
thf(1787,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)],[502]) ).
thf(265,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(1210,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(757,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)],[60]) ).
thf(21,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(682,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(415,axiom,
class_Nat_Osemiring__char__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Nat_Osemiring__char__0) ).
thf(1573,plain,
class_Nat_Osemiring__char__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(566,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(1938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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)],[109]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__mult__distrib_0) ).
thf(1837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(427,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/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
thf(1602,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)],[427]) ).
thf(578,axiom,
class_Ring__and__Field_Oring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) ).
thf(1968,plain,
class_Ring__and__Field_Oring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(124,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(879,plain,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(1888,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(1296,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(461,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/sandbox/benchmark/theBenchmark.p',cls_monom__eq__iff_0) ).
thf(1687,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)],[461]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(1457,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(554,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
thf(1910,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)],[554]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( 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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( 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)],[274]) ).
thf(588,axiom,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(1983,plain,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ 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)],[4]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_0) ).
thf(1328,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)],[312]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(1096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(473,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
thf(1719,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(119,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(869,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(488,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/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
thf(1755,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)],[488]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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)],[75]) ).
thf(113,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(857,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(326,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(1360,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(322,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(1350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(288,axiom,
class_OrderedGroup_Omonoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
thf(1270,plain,
class_OrderedGroup_Omonoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(495,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
thf(1772,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)],[495]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( c_Suc @ D ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( c_Suc @ D ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(400,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 )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(1534,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 )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(505,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1794,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(188,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(1017,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(383,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1498,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
thf(1587,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_Osmult @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__smult_0) ).
thf(1540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_Osmult @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(1006,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(458,axiom,
class_Ring__and__Field_Ocomm__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
thf(1683,plain,
class_Ring__and__Field_Ocomm__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(127,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(884,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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)],[127]) ).
thf(214,axiom,
! [A: $i] :
( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
thf(1082,plain,
! [A: $i] :
( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(327,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(1361,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(150,axiom,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
thf(933,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)],[150]) ).
thf(58,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__semidom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
thf(753,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)],[58]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(1075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(1424,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(642,axiom,
class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
thf(2080,plain,
class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(1584,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(466,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
thf(1700,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)],[466]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(1644,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(349,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(1414,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(626,axiom,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(2053,plain,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(526,axiom,
! [A: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(1842,plain,
! [A: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(187,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
thf(1016,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(1207,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(19,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(679,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ B ) @ ( c_Polynomial_Osmult @ C @ D @ A ) )
!= ( c_Polynomial_OpCons @ E @ D @ A ) )
| ( E
= ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
thf(970,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ B ) @ ( c_Polynomial_Osmult @ C @ D @ A ) )
!= ( c_Polynomial_OpCons @ E @ D @ A ) )
| ( E
= ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(1155,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)],[243]) ).
thf(483,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(1744,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(518,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(1825,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(221,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 )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(1099,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 )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(6,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(654,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)],[6]) ).
thf(583,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ C )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Polynomial_Oorder @ C @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_2) ).
thf(1974,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ B @ A ) @ C )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Polynomial_Oorder @ C @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(172,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
thf(984,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)],[172]) ).
thf(599,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__monom_0) ).
thf(2006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(589,axiom,
class_OrderedGroup_Osemigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__add) ).
thf(1984,plain,
class_OrderedGroup_Osemigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(530,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) @ C )
!= C )
| ( ( c_Polynomial_Opoly__rec @ C @ B @ ( c_Polynomial_OpCons @ D @ E @ A ) @ F @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ B @ D ) @ E ) @ ( c_Polynomial_Opoly__rec @ C @ B @ E @ F @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__rec__pCons_0) ).
thf(1852,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) @ C )
!= C )
| ( ( c_Polynomial_Opoly__rec @ C @ B @ ( c_Polynomial_OpCons @ D @ E @ A ) @ F @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ B @ D ) @ E ) @ ( c_Polynomial_Opoly__rec @ C @ B @ E @ F @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(1874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1429,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(1720,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(340,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(1393,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(2,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(647,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(1263,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(179,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(997,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(1530,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(1382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(286,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1266,plain,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(1231,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(205,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).
thf(1060,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)],[205]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',cls_pcompose__0_0) ).
thf(1050,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)],[201]) ).
thf(625,axiom,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(2052,plain,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(426,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(1599,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(586,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
thf(1979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(73,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(779,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(592,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(1991,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(1779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(86,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
thf(805,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)],[86]) ).
thf(620,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
thf(2043,plain,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(464,axiom,
! [D: $i,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 @ A ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Osmult @ D @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ D @ A ) @ A ) ) @ ( c_Polynomial_OpCons @ B @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ D @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__pCons_0) ).
thf(1695,plain,
! [D: $i,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 @ A ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_Osmult @ D @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ D @ A ) @ A ) ) @ ( c_Polynomial_OpCons @ B @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ D @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(8,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(657,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(640,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2 @ A )
!= ( c_HOL_Ozero__class_Ozero @ t_a ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ A @ t_a ) @ t_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__decompose_0) ).
thf(2076,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2 @ A )
!= ( c_HOL_Ozero__class_Ozero @ t_a ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ A @ t_a ) @ t_a @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(256,axiom,
class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
thf(1187,plain,
class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(1663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(1167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__one__right_0) ).
thf(953,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(595,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3 @ A ) @ t_a ) ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1 @ A ) ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ A @ t_a ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ A @ t_a ) @ t_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__decompose_2) ).
thf(1996,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3 @ A ) @ t_a ) ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1 @ A ) ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ A @ t_a ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ A @ t_a ) @ t_a @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_OpCons @ B @ C @ A ) @ A ) @ ( c_Suc @ D ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__pCons__Suc_0) ).
thf(1846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_OpCons @ B @ C @ A ) @ A ) @ ( c_Suc @ D ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(1054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(1035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(718,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(129,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(888,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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)],[129]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( 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)],[139]) ).
thf(457,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ B ) @ C ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__add_0) ).
thf(1680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ B ) @ C ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(1698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(269,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(1219,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(1301,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(24,axiom,
class_Ring__and__Field_Opordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
thf(689,plain,
class_Ring__and__Field_Opordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(332,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(965,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)],[164]) ).
thf(56,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(750,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ A @ B @ C ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power_Opower_Opower__0_0) ).
thf(1510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ A @ B @ C ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__Suc2_0) ).
thf(1251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(491,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
thf(1764,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)],[491]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(694,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)],[27]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(1916,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(732,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)],[48]) ).
thf(69,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(772,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Suc @ ( c_Polynomial_Odegree @ B @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__def_1) ).
thf(1620,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Suc @ ( c_Polynomial_Odegree @ B @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(1929,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(605,axiom,
class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(2016,plain,
class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(1388,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(743,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)],[53]) ).
thf(506,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1795,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)],[506]) ).
thf(577,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(1965,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(232,axiom,
! [A: $i] :
( ( class_OrderedGroup_Osemigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Osemigroup__add) ).
thf(1124,plain,
! [A: $i] :
( ( class_OrderedGroup_Osemigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(1488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(975,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(875,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)],[122]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(826,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(36,axiom,
class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
thf(711,plain,
class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(452,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Osemiring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__1) ).
thf(1669,plain,
! [A: $i] :
( ( class_Ring__and__Field_Osemiring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(612,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(2029,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(1707,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
thf(1271,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(1312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(77,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
thf(787,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)],[77]) ).
thf(439,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
thf(1635,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(1107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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)],[224]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(628,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
thf(2055,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(1090,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(549,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(1897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(440,axiom,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(1638,plain,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(1464,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(157,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_OpCons @ B @ C @ A ) ) @ ( c_Polynomial_OpCons @ D @ E @ A ) )
= ( c_Polynomial_OpCons @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ C ) @ E ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pCons_0) ).
thf(947,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Polynomial_OpCons @ B @ C @ A ) ) @ ( c_Polynomial_OpCons @ D @ E @ A ) )
= ( c_Polynomial_OpCons @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ A ) ) @ C ) @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(764,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)],[64]) ).
thf(641,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(2079,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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)],[136]) ).
thf(20,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(681,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(293,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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
thf(1282,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)],[293]) ).
thf(645,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(2084,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(547,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(1894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(1117,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
| ( c_lessequals @ B @ A @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
thf(1492,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
| ( c_lessequals @ B @ A @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(1722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(50,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
thf(737,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)],[50]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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)],[125]) ).
thf(230,axiom,
class_Power_Opower @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
thf(1122,plain,
class_Power_Opower @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(1690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(414,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(1571,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(579,axiom,
! [A: $i] :
( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
thf(1969,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)],[579]) ).
thf(304,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
thf(1307,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)],[304]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ 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/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ 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)],[116]) ).
thf(632,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(2065,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(890,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)],[130]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(811,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)],[89]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(1877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(610,axiom,
! [B: $i,A: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 @ A @ B ) @ tc_Complex_Ocomplex )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset_0) ).
thf(2025,plain,
! [B: $i,A: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 @ A @ B ) @ tc_Complex_Ocomplex )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(92,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(816,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(478,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(1731,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(534,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(1862,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(30,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(700,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) @ C )
!= C )
| ( ( c_Polynomial_Opoly__rec @ C @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ D @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__rec__0_0) ).
thf(1325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) @ C )
!= C )
| ( ( c_Polynomial_Opoly__rec @ C @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ D @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(133,axiom,
class_OrderedGroup_Opordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
thf(895,plain,
class_OrderedGroup_Opordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(1344,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(943,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)],[155]) ).
thf(335,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) ).
thf(1381,plain,
class_Ring__and__Field_Osemiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(1952,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(516,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(1820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ 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)],[516]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(437,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(1630,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(594,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( hAPP @ ( c_Polynomial_Opoly @ A @ t_a ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ t_a ) @ ( hAPP @ ( c_Polynomial_Opoly @ A @ t_a ) @ ( c_HOL_Ozero__class_Ozero @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ B ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1 @ A ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2 @ A ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3 @ A ) @ t_a ) @ t_a ) @ B ) ) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ A @ t_a ) @ t_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__decompose_3) ).
thf(1993,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( hAPP @ ( c_Polynomial_Opoly @ A @ t_a ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ t_a ) @ ( hAPP @ ( c_Polynomial_Opoly @ A @ t_a ) @ ( c_HOL_Ozero__class_Ozero @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ B ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1 @ A ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2 @ A ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3 @ A ) @ t_a ) @ t_a ) @ B ) ) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ A @ t_a ) @ t_a @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(83,axiom,
class_Ring__and__Field_Omult__mono @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
thf(799,plain,
class_Ring__and__Field_Omult__mono @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(44,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(726,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(408,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/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).
thf(1556,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)],[408]) ).
thf(67,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
thf(769,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(367,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
thf(1460,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)],[367]) ).
thf(298,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
thf(1293,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(668,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( 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)],[13]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(912,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(639,axiom,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(2075,plain,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(561,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(1926,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(1594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(959,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(397,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(1528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(631,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(2064,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_1) ).
thf(1176,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)],[252]) ).
thf(173,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(986,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(357,axiom,
( ~ ( class_HOL_Ozero @ t_a )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ v_p @ t_a )
= ( c_HOL_OIf @ ( c_fequal @ v_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) @ ( tc_Polynomial_Opoly @ t_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_Polynomial_Odegree @ v_p @ t_a ) ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__def__raw_0) ).
thf(1435,plain,
( ~ ( class_HOL_Ozero @ t_a )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ v_p @ t_a )
= ( c_HOL_OIf @ ( c_fequal @ v_p @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) @ ( tc_Polynomial_Opoly @ t_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_Polynomial_Odegree @ v_p @ t_a ) ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(609,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Oring__char__0 @ A )
| ( ( c_Polynomial_Opoly @ B @ A )
!= ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__zero_0) ).
thf(2022,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Oring__char__0 @ A )
| ( ( c_Polynomial_Opoly @ B @ A )
!= ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(1364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(410,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/sandbox/benchmark/theBenchmark.p',cls_offset__poly__0_0) ).
thf(1562,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)],[410]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(1198,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
thf(1396,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)],[341]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(1044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Ocoeff @ B @ A )
!= ( c_Polynomial_Ocoeff @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__inject_0) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Ocoeff @ B @ A )
!= ( c_Polynomial_Ocoeff @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(1102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(582,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(1973,plain,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(1805,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(636,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(2069,plain,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(658,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)],[9]) ).
thf(17,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(675,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(512,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(1809,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(1758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(1467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(795,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)],[81]) ).
thf(552,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(1905,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( 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)],[552]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( 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)],[148]) ).
thf(459,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(1684,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(389,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
thf(1509,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(372,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
thf(1472,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(627,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(2054,plain,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(722,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(303,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(1304,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(538,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(1873,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(153,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) ).
thf(939,plain,
class_Ring__and__Field_Osemiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(317,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_OrderedGroup_Ocomm__monoid__add__axioms @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add__class_Oaxioms_0) ).
thf(1340,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_OrderedGroup_Ocomm__monoid__add__axioms @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(102,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Opordered__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
thf(836,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)],[102]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(1551,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(485,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(1748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(1025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
thf(1225,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)],[271]) ).
thf(603,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(2012,plain,
class_Power_Opower @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__one_0) ).
thf(1605,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(444,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(1647,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(51,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(739,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(220,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1098,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(177,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
thf(993,plain,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(712,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(1770,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(25,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(690,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).
thf(1516,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)],[393]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(705,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)],[33]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(1753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(1267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( 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)],[287]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ 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)],[16]) ).
thf(356,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/sandbox/benchmark/theBenchmark.p',cls_monom__Suc_0) ).
thf(1432,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)],[356]) ).
thf(364,axiom,
! [A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ ( c_Polynomial_Odegree @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_1) ).
thf(1452,plain,
! [A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ ( c_Polynomial_Odegree @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(79,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(791,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(1188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1038,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)],[197]) ).
thf(621,axiom,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ v_q____ @ tc_Complex_Ocomplex )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ v_pa____ @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_q_I1_J_0) ).
thf(2044,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ v_q____ @ tc_Complex_Ocomplex )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ v_pa____ @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(1579,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(202,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1053,plain,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(384,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(1499,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(1790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(1716,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(104,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(840,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(501,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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
thf(1785,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)],[501]) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
thf(1317,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)],[308]) ).
thf(521,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(1738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(268,axiom,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).
thf(1218,plain,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(564,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(1934,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(467,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__0_0) ).
thf(1702,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(294,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(1284,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)],[294]) ).
thf(573,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
thf(1955,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)],[573]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(1427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(1797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(1008,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(613,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
thf(2030,plain,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ 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)],[114]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
thf(1404,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(1358,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ 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)],[325]) ).
thf(403,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/sandbox/benchmark/theBenchmark.p',cls_monom__0_0) ).
thf(1543,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)],[403]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(1766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(529,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(1849,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(7,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(656,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(1802,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(1023,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(1485,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(581,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
thf(1972,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(388,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__monom_0) ).
thf(1506,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(386,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(1504,plain,
class_OrderedGroup_Osemigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(45,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(727,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(1140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(567,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__add_0) ).
thf(1940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(108,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
thf(845,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)],[108]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(1949,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(15,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Opordered__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
thf(671,plain,
! [A: $i] :
( ( class_Ring__and__Field_Opordered__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(527,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(1844,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(61,axiom,
class_Ring__and__Field_Omult__mono @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(759,plain,
class_Ring__and__Field_Omult__mono @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(233,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(1126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(362,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1448,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(107,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(844,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(352,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1421,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(604,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ A @ C ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ A @ t_a @ t_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_constant__def_0) ).
thf(2013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ A @ C ) )
| ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ A @ t_a @ t_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(445,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
thf(1649,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)],[445]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(1834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(556,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(1913,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(447,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/sandbox/benchmark/theBenchmark.p',cls_degree__monom__eq_0) ).
thf(1654,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)],[447]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(185,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/sandbox/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)],[185]) ).
thf(339,axiom,
! [A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__power__power_0) ).
thf(1390,plain,
! [A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(479,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/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1734,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)],[479]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(1807,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(1476,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_0) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( hAPP @ ( c_Polynomial_Ocoeff @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(156,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(946,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(517,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/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0__iff_0) ).
thf(1822,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)],[517]) ).
thf(74,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Omult__mono1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
thf(781,plain,
! [A: $i] :
( ( class_Ring__and__Field_Omult__mono1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(1276,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__eq__0__iff_0) ).
thf(1590,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(162,axiom,
class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
thf(961,plain,
class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(813,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( 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)],[90]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( 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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(1385,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( 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)],[337]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(748,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(454,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(1674,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(441,axiom,
! [A: $i] :
( ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).
thf(1639,plain,
! [A: $i] :
( ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(643,axiom,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nc_0) ).
thf(2081,plain,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ v_pa____ @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(619,axiom,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ v_p @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_0) ).
thf(2041,plain,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ ( c_Polynomial_Opoly @ v_p @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(497,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1777,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(1294,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(633,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(2066,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(1193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
thf(1212,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)],[266]) ).
thf(392,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/sandbox/benchmark/theBenchmark.p',cls_degree__offset__poly_0) ).
thf(1513,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)],[392]) ).
thf(99,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(832,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(1444,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Oring__char__0 @ A )
| ( ( c_Polynomial_Opoly @ B @ A )
!= ( c_Polynomial_Opoly @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__iff_0) ).
thf(2019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Oring__char__0 @ A )
| ( ( c_Polynomial_Opoly @ B @ A )
!= ( c_Polynomial_Opoly @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(600,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(2009,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(533,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(1861,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(617,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
thf(2036,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
thf(1309,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)],[305]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(716,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)],[39]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
thf(1161,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)],[246]) ).
thf(431,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(1614,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(84,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
thf(800,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(1348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(57,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
thf(752,plain,
class_Ring__and__Field_Omult__mono1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(476,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(1725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(1957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(950,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(404,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/sandbox/benchmark/theBenchmark.p',cls_offset__poly__single_0) ).
thf(1546,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)],[404]) ).
thf(435,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__smult_0) ).
thf(1625,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(93,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(818,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ 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)],[93]) ).
thf(423,axiom,
class_HOL_Ozero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
thf(1593,plain,
class_HOL_Ozero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(118,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Omult__mono @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
thf(867,plain,
! [A: $i] :
( ( class_Ring__and__Field_Omult__mono @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(865,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(735,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)],[49]) ).
thf(553,axiom,
! [A: $i] :
( ( class_Nat_Osemiring__char__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Nat_Osemiring__char__0) ).
thf(1908,plain,
! [A: $i] :
( ( class_Nat_Osemiring__char__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
thf(2003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ B @ C @ A ) @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(391,axiom,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
thf(1512,plain,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(1774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(100,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(833,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( 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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( 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)],[279]) ).
thf(624,axiom,
( v_n____
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ v_pa____ @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n_0) ).
thf(2050,plain,
( v_n____
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ v_pa____ @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(1314,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( 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)],[307]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( A
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(1495,plain,
! [B: $i,A: $i] :
( ( A
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(1657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(87,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
thf(807,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)],[87]) ).
thf(11,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(664,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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)],[11]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(828,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(1473,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(1065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(28,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(696,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(41,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(720,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( 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)],[128]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
thf(1693,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(637,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2 @ A )
!= ( c_HOL_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ A @ t_a ) @ B )
= ( c_HOL_Ozero__class_Ozero @ t_a ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__decompose__lemma_0) ).
thf(2070,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ t_a )
| ( ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2 @ A )
!= ( c_HOL_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ A @ t_a ) @ B )
= ( c_HOL_Ozero__class_Ozero @ t_a ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(1172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(767,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(1288,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(470,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(1710,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(218,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(1093,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(728,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)],[46]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(1352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
thf(1532,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(1537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(419,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(1582,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(560,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(1925,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(1713,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(182,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(1004,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( 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)],[182]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(1299,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(551,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(1902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(1885,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(120,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(871,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(520,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(1829,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(584,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(1977,plain,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(234,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(1129,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(1827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(284,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(1261,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ 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)],[140]) ).
thf(176,axiom,
class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
thf(992,plain,
class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(387,axiom,
class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
thf(1505,plain,
class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(342,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
thf(1399,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)],[342]) ).
thf(313,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
thf(1331,plain,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(151,axiom,
class_HOL_Ozero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
thf(935,plain,
class_HOL_Ozero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(607,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(2018,plain,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(126,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ A @ B @ C ) @ D ) @ ( c_Suc @ E ) )
= ( hAPP @ ( hAPP @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ A @ B @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power_Opower_Opower__Suc_0) ).
thf(882,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ A @ B @ C ) @ D ) @ ( c_Suc @ E ) )
= ( hAPP @ ( hAPP @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ A @ B @ C ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(1870,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(1367,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(940,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
thf(923,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)],[146]) ).
thf(480,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(1737,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(1490,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(196,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1037,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(775,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)],[71]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
thf(1204,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)],[263]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(1449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(513,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/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
thf(1812,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)],[513]) ).
thf(34,axiom,
class_Ring__and__Field_Oordered__idom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
thf(708,plain,
class_Ring__and__Field_Oordered__idom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(555,axiom,
class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
thf(1912,plain,
class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(2085,plain,
$false,
inference(e,[status(thm)],[892,1322,1469,760,2031,1633,1237,1179,1549,1554,1686,1501,809,1879,1337,1559,1105,893,1840,962,1982,666,1818,1855,1750,1158,683,1068,1522,994,1401,1569,1728,873,1142,677,1596,1406,730,1882,741,1073,1971,1793,1041,861,1705,1078,1671,1608,1137,2035,1867,698,670,1164,1999,797,1919,1988,1761,1342,1222,930,1196,1001,2046,1782,1441,709,841,973,2067,1746,898,2010,1935,1228,1623,1482,1254,1628,1985,2039,1660,785,838,802,1279,1992,1409,724,917,702,1577,1455,1832,1191,1462,1132,1800,1087,1479,1741,1115,1931,1641,1963,1922,902,1892,1379,1319,1890,969,1347,1013,770,1815,1494,1946,2027,789,1373,1109,1418,834,1978,1151,1020,1677,1960,2073,2017,1334,646,1858,1864,2058,1377,1215,998,988,981,766,1169,687,1896,877,692,1447,956,1119,774,1943,1201,1242,849,1651,2011,920,793,925,761,2047,1783,2083,1438,661,1768,714,2061,2000,1047,1057,1274,746,778,1519,1355,1123,820,1666,1370,1900,910,1174,1676,2032,815,1951,2068,830,1159,1787,1210,757,682,1291,1573,1938,847,1837,1602,1968,879,1888,1296,1687,1457,1079,1027,1910,842,1234,1983,650,1328,1096,1719,869,1755,783,857,1360,1350,1270,1772,1259,1534,1794,1017,1498,1587,1540,1006,1567,1683,884,1082,1361,933,753,1182,1075,1424,2080,1584,1700,1644,1414,2053,1842,1016,1207,679,970,1155,1744,1825,1099,654,1974,984,2006,1984,1852,1874,1429,1720,1393,1525,647,1263,997,1530,1382,1266,1231,1060,1050,2052,1599,1979,779,1991,1779,805,2043,1695,657,2076,1071,1187,1663,1167,953,1996,1846,1054,1286,1035,718,888,906,1680,1698,1219,1301,689,1374,965,750,1510,1251,1764,694,1916,732,772,1620,1929,2016,1388,743,1795,1965,1124,1488,904,975,875,826,711,1669,936,2029,1707,1271,1312,787,1635,1107,1332,2055,1090,1897,1638,1464,947,764,2079,900,681,1282,2084,1894,1117,1574,990,1492,1722,737,880,1122,1690,1571,1969,1307,863,2065,890,811,1877,2025,816,1731,1862,700,1325,895,1344,943,1381,1952,1820,1112,1630,1993,799,726,1556,769,1460,1293,668,912,2075,1926,1594,959,1528,2064,1176,986,1435,2022,1364,1562,1198,1396,1044,1245,851,1102,1973,1805,2069,658,675,1809,1758,1467,795,1905,927,1684,1509,1472,1145,2054,722,1304,1873,1134,648,939,1340,836,1551,1748,1025,1225,2012,1605,1647,739,1098,993,712,1770,690,1516,705,1611,1753,1267,673,1432,1452,791,1188,1038,2044,1579,1053,1499,1790,1716,840,1785,1317,1830,1738,1218,1934,703,1702,1284,1955,1427,1797,1008,2030,859,1404,1358,1543,1766,1849,1257,656,1802,1023,1485,1972,1506,1504,727,978,1140,1240,1617,1940,845,1949,671,1844,759,1126,1448,844,1421,2013,1649,1084,1834,1913,1654,1412,1010,1390,1734,1807,1476,1062,946,652,1822,781,1276,1590,961,813,1385,896,748,1674,1639,1030,2081,914,2041,1777,1294,2066,1193,1212,1513,832,1444,2019,2009,1861,2036,1309,716,1161,1614,800,1348,752,1725,1957,950,1546,1625,818,1593,854,1148,867,865,735,1908,2003,1512,1774,833,967,1248,2050,1314,1495,1657,807,664,828,1473,1065,696,720,886,1693,2070,1172,1410,767,1033,1288,1710,1093,728,1352,1532,1537,1582,822,1925,1713,1004,1299,1902,1885,871,1829,1977,1129,1827,1261,908,992,1505,1399,1331,935,1184,1565,2018,1416,755,882,1870,1367,940,923,1737,1490,1037,775,1204,1449,1812,708,1912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG397-1 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 23:47:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.92/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.81/1.08 % [INFO] Parsing done (234ms).
% 1.81/1.09 % [INFO] Running in sequential loop mode.
% 2.24/1.30 % [INFO] eprover registered as external prover.
% 2.24/1.31 % [INFO] cvc4 registered as external prover.
% 2.24/1.31 % [INFO] Scanning for conjecture ...
% 2.52/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 712 axioms. Running axiom selection ...
% 3.32/1.57 % [INFO] Axiom selection finished. Selected 644 axioms (removed 68 axioms).
% 3.72/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 3.72/1.75 % [INFO] Type checking passed.
% 3.72/1.76 % [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 ...
% 10.60/3.34 % External prover 'e' found a proof!
% 10.60/3.34 % [INFO] Killing All external provers ...
% 10.60/3.35 % Time passed: 2832ms (effective reasoning time: 2252ms)
% 10.60/3.35 % Axioms used in derivation (644): cls_poly__decompose__lemma_0, cls_offset__poly__eq__0__iff_0, cls_add__0__left_0, cls_add__Suc__shift_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oidom, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_minus__le__iff_0, cls_power__0_0, cls_natgb_Oadd__r0__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict, cls_pCons__0__0_0, cls_neg__0__le__iff__le_1, cls_comm__monoid__add_Opower__mult__distrib_0, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_add__is__1_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_of__nat__add_0, cls_smult__monom_0, cls_Suc__inject_0, cls_comm__semiring__class_Odistrib_0, cls_poly__decompose_2, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_of__nat__0_0, cls_smult__smult_0, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_offset__poly__pCons_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_degree__pCons__eq_0, cls_le__minus__self__iff_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors, cls_sum__squares__eq__zero__iff_0, cls_Suc__n__not__n_0, cls_left__minus_0, cls_square__eq__iff_1, cls_class__semiring_Osemiring__rules_I9_J_0, cls_minus__zero_0, cls_power__eq__0__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oring, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_pcompose__0_0, cls_one__is__add_4, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1, cls_assms_0, cls_poly__offset_0, cls_degree__pCons__0_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_not__sum__squares__lt__zero_0, cls_pos__add__strict_0, cls_degree__smult__eq_1, cls_add__increasing2_0, cls_monoid__add__class_Oaxioms_0, cls_add__is__1_2, cls_power__inject__exp_0, cls_zero__le__mult__iff_3, cls_add__strict__right__mono_0, clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add, cls_CHAINED_0, clsarity_Polynomial__Opoly__Nat_Osemiring__char__0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_poly__rec__0_0, cls_power__le__zero__eq_3, cls_class__semiring_Osemiring__rules_I21_J_0, cls_minus__add__distrib_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_add__is__0_0, cls_class__semiring_Osemiring__rules_I10_J_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_add__imp__eq_0, clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add, cls_add__le__cancel__right_1, cls_minus__le__self__iff_0, cls_add__le__cancel__left_1, cls_real__le__trans_0, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, cls_one__is__add_1, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_mult__nonpos__nonpos_0, cls_class__ringb_Onoteq__reduce_0, cls_comm__monoid__add_Omult__1__right_0, cls_minus__minus_0, cls_le__eq__neg_0, cls_comm__monoid__add_Omult__assoc_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_neg__less__iff__less_1, cls_comm__monoid__add__class_Oaxioms_0, cls_add__cancel__21_1, cls_less__minus__iff_0, cls_mult__le__cancel__left__pos_0, cls_sum__squares__ge__zero_0, cls_power__one_0, cls_power__gt1_0, cls_add__nonpos__neg_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add, clsarity_nat__HOL_Ozero, cls_mult__less__imp__less__right_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_minus__unique_0, cls_split__mult__neg__le_0, cls_poly__monom_0, cls_mult__less__imp__less__left_0, cls_coeff__smult_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, cls_add__nonneg__pos_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0, cls_sum__squares__le__zero__iff_1, cls_mult__less__cancel__right__disj_3, clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_mult__eq__0__iff_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_monom__eq__iff_0, cls_smult__pCons_0, cls_mult__mono_0, cls_ab__left__minus_0, cls_neg__equal__iff__equal_0, cls_one__le__power_0, clsarity_nat__OrderedGroup_Omonoid__mult, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add, cls_double__add__less__zero__iff__single__less__zero_0, cls_add__right__mono_0, cls_smult__eq__0__iff_1, cls_poly__add_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_nc_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_field__power__not__zero_0, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_psize__def_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_mult__left__mono__neg_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring, clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__1, cls_power_Opower_Opower__0_0, cls_coeff__monom_1, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_mult_Ozero__left_0, cls_n_0, cls_mult__pos__neg_0, cls_zero__le__mult__iff_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__left__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, cls_real__le__linear_0, cls_mult__strict__right__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Omul__c_0, cls_mult_Oadd__left_0, cls_mult__strict__mono_0, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, cls_poly__pcompose_0, clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1, cls_mult_Ozero__right_0, cls_add__cancel__end_0, cls_neg__0__le__iff__le_0, cls_minus__less__iff_1, cls_power__le__zero__eq_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_foldl__absorb0_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add, cls_monom__Suc_0, cls_add__Suc_0, cls_mult__right_Oadd_0, cls_minus__add__cancel_0, cls_power__Suc2_0, 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_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_poly__rec_Osimps_0, cls_add__nonneg__eq__0__iff_0, cls_add__less__cancel__right_1, cls_order__root_0, clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__add, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_comm__monoid__add_Opower__commutes_0, cls_degree__0_0, cls_no__zero__divisors_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, cls_one__is__add_5, cls_class__semiring_Osemiring__rules_I6_J_0, cls_comm__monoid__add_Opower__Suc_0, cls_zero__le__double__add__iff__zero__le__single__add_1, clsarity_Polynomial__Opoly__HOL_Ozero, cls_coeff__0_0, cls_le__minus__iff_0, cls_add__left__mono_0, cls_nat__add__left__commute_0, cls_degree__smult__eq_0, cls_zero__le__mult__iff_4, cls_power__gt1__lemma_0, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult, cls_class__semiring_Osemiring__rules_I2_J_0, cls_mult__1__right_0, cls_add__strict__left__mono_0, cls_of__nat__0__le__iff_0, cls_real__le__refl_0, cls_combine__common__factor_0, cls_pCons__eq__0__iff_1, cls_of__nat__1_0, cls_leading__coeff__0__iff_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_power__0__Suc_0, cls_mult__le__0__iff_0, cls_add__le__less__mono_0, cls_mult__neg__pos_0, cls_poly__offset_1, cls_mult__right__le__imp__le_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring, cls_Suc__neq__Zero_0, cls_power__eq__0__iff_2, cls_monom__0_0, cls_class__ringb_Onoteq__reduce_1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add, cls_neg__le__0__iff__le_0, cls_le__eq__neg_1, 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__mono1_0, cls_mult__less__cancel__left__disj_0, cls_class__semiring_Oadd__a_0, cls_minus__mult__commute_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_le__minus__iff_1, cls_one__is__add_0, clsarity_Complex__Ocomplex__Nat_Osemiring__char__0, clsarity_RealDef__Oreal__Nat_Osemiring__char__0, cls_calculation_0, cls_class__semiring_Osemiring__rules_I19_J_0, clsarity_nat__Ring__and__Field_Opordered__cancel__semiring, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add, cls_mult__le__cancel__left__neg_1, cls_of__nat__eq__iff_0, clsarity_Complex__Ocomplex__Int_Oring__char__0, cls_smult__0__left_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add, cls_add__right__cancel_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1, cls_mult__le__cancel__left__pos_1, cls_mult__le__0__iff_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_split__mult__pos__le_0, cls_sum__squares__le__zero__iff_2, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring, cls_zero__le__power__iff_1, cls_class__semiring_Osemiring__rules_I17_J_0, cls_class__semiring_Oadd__0_0, clsarity_nat__Nat_Osemiring__char__0, cls_power__less__power__Suc_0, cls_poly__pCons_0, cls_comm__monoid__add_Omult__commute_0, clsarity_RealDef__Oreal__Power_Opower, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add, cls_nat__add__assoc_0, cls_zero__less__two_0, cls_mult_Ominus__right_0, cls_comm__monoid__add_Opower__one__right_0, clsarity_RealDef__Oreal__Int_Oring__char__0, cls_class__ringb_Oadd__mul__solve_0, cls_add__strict__mono_0, cls_neg__0__less__iff__less_0, cls_comm__monoid__add_Opower__one_0, cls_neg__less__0__iff__less_0, cls_sum__squares__eq__zero__iff_1, clsarity_nat__Ring__and__Field_Omult__mono, cls_neg__equal__0__iff__equal_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__1, cls_mult__le__0__iff_4, cls_comm__monoid__add_Opower__0_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors, cls_le__minus__self__iff_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict, cls_One__nat__def_0, cls_smult__1__left_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, cls_less__add__one_0, cls_mult__less__cancel__right__disj_2, cls_zero__less__power_0, cls_minus__le__self__iff_1, cls_add__cancel__21_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_poly__eq__iff_0, cls_mult__left__less__imp__less_0, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_class__semiring_Omul__d_0, cls_monom__eq__0__iff_0, cls_zero__less__power__eq_3, cls_power_Opower_Opower__Suc_0, cls_offset__poly__eq__0__lemma_0, cls_coeff__monom_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_comm__monoid__add_Opower__add_0, cls_no__zero__divirors__neq0_0, cls_mult__le__0__iff_5, cls_mult__strict__mono_H_0, cls_zero__neq__one_0, cls_poly__0_0, cls_class__semiring_Osemiring__rules_I5_J_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one, clsarity_Polynomial__Opoly__Power_Opower, cls_split__mult__pos__le_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict, cls_mult__right_Ominus_0, cls_power__Suc_0, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add, cls_natgb_Oadd__cancel_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_smult__add__left_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add, cls_less__1__mult_0, 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cls_synthetic__div__unique_0, cls_neg__0__equal__iff__equal_1, cls_class__semiring_Omul__1_0, cls_zero__le__double__add__iff__zero__le__single__add_0, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring, cls_mult__nonneg__nonpos_0, cls_foldl__assoc_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, cls_class__semiring_Osemiring__rules_I23_J_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono, cls_linorder__neqE__ordered__idom_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1, cls_class__ringb_Oadd__cancel_0, clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring, cls_add__nonneg__eq__0__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring, cls_not__square__less__zero_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add, clsarity_nat__OrderedGroup_Oab__semigroup__mult, clsarity_RealDef__Oreal__Ring__and__Field_Oidom, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_mult__left__le__one__le_0, cls_add__nonpos__nonpos_0, cls_class__semiring_Osemiring__rules_I3_J_0, cls_mult__eq__0__iff_2, cls_sum__squares__gt__zero__iff_1, cls_add__nonneg__nonneg_0, cls_neg__le__0__iff__le_1, cls_mult__strict__left__mono__comm_0, cls_class__ringb_Oadd__r0__iff_0, cls_nat_Oinject_0, cls_pc0_0, cls_psize__eq__0__iff_0, cls_even__less__0__iff_1, cls_class__ring_Oneg__mul_0, cls_coeff__inject_0, clsarity_nat__Ring__and__Field_Osemiring, cls_eq__neg__iff__add__eq__0_1, cls_mult__mono_H_0, cls_c_0, cls_add__pCons_0, cls_mult__less__cancel__left__neg_1, cls_add__strict__increasing_0, cls_le__imp__neg__le_0, cls_power__le__imp__le__base_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring, cls_smult__add__right_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add, 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clsarity_RealDef__Oreal__Ring__and__Field_Osemiring, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_neg__less__0__iff__less_1, cls_mult__right__mono__neg_0, cls_sum__squares__eq__zero__iff_2, cls_add__minus__cancel_0, cls_real__le__antisym_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_pCons__eq__0__iff_0, cls_mult__less__cancel__left__disj_3, cls_zero__less__mult__pos2_0, cls_mult__left_Ominus_0, cls_pCons__eq__iff_1, cls_mult_Oadd__right_0, cls_coeff__pCons__Suc_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, cls_zero__less__power__eq_2, cls_comm__monoid__add_Omult__left__commute_0, cls_le__add__right__mono_0, cls_minus__mult__right_0, cls_mult__1_0, cls_q_I1_J_0, clsarity_nat__Ring__and__Field_Omult__mono1, cls_minus__le__iff_1, cls_mult__1__left_0, cls_class__semiring_Osemiring__rules_I35_J_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring, cls_nat_Osimps_I3_J_0, cls_q_I2_J_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add, cls_comm__monoid__add_Omult__1_0, clsarity_Polynomial__Opoly__Int_Onumber__ring, 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_mult__zero__left_0, cls_plus__nat_Oadd__0_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, cls_poly__decompose_3, cls_add__nonneg__eq__0__iff_2, cls_add__is__0_2, cls_power__eq__0__iff_0, cls_class__semiring_Oadd__c_0, cls_power__Suc__less__one_0, cls_add__poly__code_I1_J_0, cls_neg__0__equal__iff__equal_0, cls_mult__left__le__imp__le_0, cls_neg__le__iff__le_0, cls_add__is__1_3, cls_add__poly__code_I2_J_0, cls_class__semiring_Osemiring__rules_I27_J_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_mult__pos__pos_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_add__eq__self__zero_0, cls_add__mono_0, cls_synthetic__div__unique__lemma_0, cls_Suc__eq__plus1_0, cls_n__not__Suc__n_0, cls_mult__right__less__imp__less_0, cls_poly__rec__pCons_0, cls_sum__squares__gt__zero__iff_0, cls_power__inject__base_0, cls_equation__minus__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring, cls_psize__def__raw_0, cls_class__semiring_Osemiring__rules_I8_J_0, cls_add__monom_0, cls_add__neg__nonpos_0, cls_add__pos__pos_0, cls_psize__def_1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0, cls_power__less__imp__less__base_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom, cls_less__minus__self__iff_0, clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add, clsarity_Complex__Ocomplex__Power_Opower, cls_offset__poly__0_0, cls_class__semiring_Opwr__mul_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_mult__less__cancel__right__disj_1, cls_add__less__cancel__left_0, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring, cls_mult__less__cancel__left__disj_2, cls_minus__add_0, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult, cls_poly__decompose_0, cls_right__minus_0, cls_one__is__add_3, cls_class__semiring_Osemiring__rules_I25_J_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring, cls_smult__eq__0__iff_0, cls_mult__eq__0__iff_1, cls_add__less__le__mono_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add, cls_zero__le__power_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, cls_minus__equation__iff_1, cls_coeff__pCons__0_0, cls_eq__neg__iff__add__eq__0_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add, cls_power__minus_0, cls_class__semiring_Opwr__0_0, clsarity_nat__Ring__and__Field_Osemiring__1, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_norm__minus__cancel_0, cls_smult__0__right_0, cls_of__nat__Suc_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring, 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_comm__monoid__add_Opower__Suc2_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__0, cls_add__strict__increasing2_0, clsarity_RealDef__Oreal__Int_Onumber__ring, cls_constant__def_0, 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_square__eq__iff_0, cls_mult__le__0__iff_3, cls_mult__neg__neg_0, cls_not__one__le__zero_0, cls_mult__less__le__imp__less_0, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_poly__zero_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1, cls_zero__le__imp__of__nat_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, clsarity_nat__OrderedGroup_Osemigroup__add, cls_power__Suc__less_0, cls_neg__less__iff__less_0, cls_even__less__0__iff_0, cls_power__0__left_1, cls_sum__squares__le__zero__iff_0, cls_add__le__cancel__right_0, cls_mult__less__cancel__left__pos_0, cls_nat__add__commute_0, cls_split__mult__neg__le_1, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1, cls_power__mono_0, cls_zero__le__mult__iff_2, cls_of__nat__less__0__iff_0, cls_coeff__add_0, cls_offset__poly__single_0, cls_mult__left_Oadd_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, clsarity_Complex__Ocomplex__HOL_Ozero, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Osemiring__rules_I22_J_0, cls_poly__offset__poly_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict
% 10.66/3.35 % No. of inferences in proof: 1291
% 10.66/3.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2832 ms resp. 2252 ms w/o parsing
% 11.21/3.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.21/3.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------