%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG401-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:46:54 AM UTC 2026
% Result : Unsatisfiable 86.02s 28.35s
% Output : Refutation 88.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1013
% Syntax : Number of formulae : 2027 ( 327 unt; 0 typ; 0 def)
% Number of atoms : 5665 (1240 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 29656 (3344 ~;3638 |; 0 &;22674 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 101 ( 99 usr; 11 con; 0-5 aty)
% Number of variables : 5274 ( 0 ^;5274 !; 0 ?;5274 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_RealVector_Onorm__class_Onorm_decl,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(c_Polynomial_Opoly_decl,type,
c_Polynomial_Opoly: $i > $i > $i > $i ).
thf(c_Polynomial_Osmult_decl,type,
c_Polynomial_Osmult: $i > $i > $i > $i ).
thf(c_HOL_Oinverse__class_Oinverse_decl,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(v_q_____decl,type,
v_q____: $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(v_w_____decl,type,
v_w____: $i ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(v_k_____decl,type,
v_k____: $i ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $i > $o ).
thf(tc_Polynomial_Opoly_decl,type,
tc_Polynomial_Opoly: $i > $i ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_HOL_Ozero_decl,type,
class_HOL_Ozero: $i > $o ).
thf(c_Polynomial_OpCons_decl,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__field_decl,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_decl,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(c_HOL_Oinverse__class_Odivide_decl,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_decl,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Odiv_decl,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Ring__and__Field_Oring__1_decl,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Polynomial_Omonom_decl,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_decl,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__0_decl,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(c_Polynomial_Opdivmod__rel_decl,type,
c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Ocancel__comm__monoid__add_decl,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
thf(c_Polynomial_Ocoeff_decl,type,
c_Polynomial_Ocoeff: $i > $i > $i > $i ).
thf(c_Polynomial_Odegree_decl,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_decl,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_decl,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_decl,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_Ring__and__Field_Odvd_decl,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Ring__and__Field_Omult__mono_decl,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_Ring__and__Field_Odivision__ring_decl,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semiring_decl,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_RealVector_Oreal__field_decl,type,
class_RealVector_Oreal__field: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: $i > $i > $i > $i ).
thf(class_RealVector_Oreal__normed__vector_decl,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(class_RealVector_Oreal__normed__div__algebra_decl,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1_decl,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1: $i > $i > $i ).
thf(c_Complex_Oexpi_decl,type,
c_Complex_Oexpi: $i > $i ).
thf(v_s_____decl,type,
v_s____: $i ).
thf(v_pa_____decl,type,
v_pa____: $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2_decl,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2: $i > $i ).
thf(530,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(2163,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(720,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(2630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
thf(1586,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(347,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(1767,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(1995,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__mult__right_0) ).
thf(1559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(631,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ ( D @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ ( A @ ( D @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( D @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__pCons_0) ).
thf(2412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ ( D @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ ( A @ ( D @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( D @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(8,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(1031,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(409,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1899,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(690,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(2559,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(684,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(2544,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_0) ).
thf(1179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(578,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(2280,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
thf(1686,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(875,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(3021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(302,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
thf(1665,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(762,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_pa____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cq0_0) ).
thf(2744,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_pa____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(1369,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(821,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(2889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(584,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(2295,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(2306,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1010,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( A @ ( F @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(3345,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( A @ ( F @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(599,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(2336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(869,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(3008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(505,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
thf(2109,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(2131,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(203,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
thf(1454,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__monom__eq_0) ).
thf(1850,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(666,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(2499,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(2427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
thf(1083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(1818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
thf(1295,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(1950,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(1549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(1855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(941,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__right_0) ).
thf(3185,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(96,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
thf(1211,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(896,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(3072,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(400,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
thf(1882,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(725,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(2644,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(960,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(3230,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(930,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
thf(3153,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(121,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1269,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(2380,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(1793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
thf(1692,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(1437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(13,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
thf(1041,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(589,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
thf(2309,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(671,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(2512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(856,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(2976,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(270,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
thf(1596,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(1406,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(2231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(717,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(2622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(624,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(2395,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(828,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_0) ).
thf(2908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(775,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(2776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(845,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(2953,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(703,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
thf(2590,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__1_1) ).
thf(1401,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(259,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1569,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(1939,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(736,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
thf(2671,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(1544,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(2014,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(1173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
thf(1486,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(1671,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
thf(1655,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(916,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
thf(3120,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(922,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(3135,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(832,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(2918,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(393,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(1867,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(520,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
thf(2141,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(751,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(2712,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_0) ).
thf(1233,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(1327,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(698,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(2580,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(804,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(2844,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(696,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(2575,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(355,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(1788,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(954,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(3217,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(886,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(3049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(60,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(1137,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(710,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(2607,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(741,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__monom_0) ).
thf(2686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__eq__0__iff_0) ).
thf(1756,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
thf(1310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(884,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(3044,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(335,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0_0) ).
thf(1735,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(74,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
thf(1164,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(592,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__cancel_0) ).
thf(2316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(2448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1007,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(3338,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(656,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(2476,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(719,axiom,
! [A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__poly__def_0) ).
thf(2627,plain,
! [A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(969,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(3253,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(2459,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(825,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__commute_0) ).
thf(2901,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(994,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(3313,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
thf(1095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1005,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(3335,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(1746,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(551,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(2216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(461,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
thf(2020,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(902,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(3088,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(491,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
thf(2082,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(1366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
thf(1803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(847,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(2957,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(2348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1012,axiom,
( ( tc_Complex_Ocomplex @ ( v_q____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lgqr_0) ).
thf(3350,plain,
( ( tc_Complex_Ocomplex @ ( v_q____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(854,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(2972,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B = C )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( C @ c_Polynomial_Ocoeff ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__dvd__antisym_0) ).
thf(2046,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B = C )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( C @ c_Polynomial_Ocoeff ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(2432,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(1914,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(556,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(2227,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(1576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(1601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(1386,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(981,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).
thf(3281,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(484,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(2067,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
thf(1529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__0_0) ).
thf(1967,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(518,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(1904,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(321,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( B @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( F @ ( C @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_0) ).
thf(1703,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( B @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( F @ ( C @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(679,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(2531,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(628,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( F @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(2405,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( F @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(115,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
thf(1254,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(129,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
thf(1287,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
thf(1709,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(878,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(3029,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(759,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(2735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(2039,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1009,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
thf(3342,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(891,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(3061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(749,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(2708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(928,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult_0) ).
thf(3148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(374,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(1826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(1279,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
thf(1132,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(747,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(2703,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(967,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(3248,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add_0) ).
thf(1409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(596,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(2328,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(831,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(2916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
thf(1660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(134,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
thf(1298,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(2339,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(885,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
thf(3046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(538,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(2185,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
thf(1455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(763,axiom,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Complex_Ocomplex @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset_0) ).
thf(2745,plain,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Complex_Ocomplex @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(608,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_Omonom ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__replicate__append_0) ).
thf(2356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_Omonom ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(809,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
= ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( E @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
thf(2857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
= ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( E @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(772,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__left_0) ).
thf(2767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(275,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1609,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(1398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
thf(1931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(2158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(290,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1641,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(349,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
thf(1773,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(807,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).
thf(2852,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(680,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(2533,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(41,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
thf(1100,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(384,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(1847,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(1892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(2169,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(627,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(2403,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(35,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(1087,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(475,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(2049,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(687,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(2552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
thf(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
thf(1890,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(836,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( F @ ( E @ ( D @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__smult__right_0) ).
thf(2929,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( F @ ( E @ ( D @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(2520,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(757,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(2730,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(553,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(999,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(3322,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(714,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(2616,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(2090,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(864,axiom,
( ( tc_Complex_Ocomplex @ ( v_q____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Complex_Ocomplex @ ( v_pa____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_q_I1_J_0) ).
thf(2996,plain,
( ( tc_Complex_Ocomplex @ ( v_q____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Complex_Ocomplex @ ( v_pa____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(778,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(2782,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
thf(1334,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(817,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
thf(2880,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(1864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(375,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(1828,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
thf(1151,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(2254,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(468,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
thf(2034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(459,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(2017,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(648,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(2456,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(453,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(2007,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(1714,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(2027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(503,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
thf(2105,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
thf(1811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
thf(1450,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
thf(1109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(1632,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(1418,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(2236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(984,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__left_0) ).
thf(3290,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(988,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(3300,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(904,axiom,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r01_0) ).
thf(3093,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(850,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
thf(2964,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(408,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(1896,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(199,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
thf(1447,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1001,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(3327,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(787,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(2804,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(770,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(2762,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(612,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(2367,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(641,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__right_0) ).
thf(2437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(894,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(3068,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(170,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
thf(1377,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(715,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(2618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(579,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(2281,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(675,axiom,
tc_Complex_Ocomplex @ class_HOL_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
thf(2523,plain,
tc_Complex_Ocomplex @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(28,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(1072,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(51,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
thf(1119,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(614,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(2371,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(965,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(3243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(789,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
thf(2809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(155,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(1345,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(785,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(2799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(581,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(2286,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(723,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(2639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(43,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(1104,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(318,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
thf(1697,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(1242,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(622,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(2392,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(1521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(753,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(2718,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(547,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(2205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(317,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1696,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(819,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(2884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
thf(1564,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(295,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
thf(1651,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(1604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(654,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(2473,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( D @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_1) ).
thf(1199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( D @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(509,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(2118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(996,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
thf(3318,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(353,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(1783,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(774,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(2773,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(929,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(3151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(456,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
thf(2011,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(906,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(3097,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(871,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(3011,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
thf(1206,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).
thf(1470,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(2093,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(492,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(2083,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(664,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_6) ).
thf(2496,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(781,axiom,
( ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_s____ @ ( v_a____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( v_w____ @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
thf(2790,plain,
( ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_s____ @ ( v_a____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( v_w____ @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(394,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(1868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(618,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(2382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(1730,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(2264,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(103,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1223,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
thf(1091,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(708,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(2601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(691,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(2560,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(2249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(1255,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(1217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(853,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
thf(2969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(968,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
thf(3250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(678,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).
thf(2528,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(401,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
thf(1883,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(683,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
thf(2541,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(705,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(2596,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(1355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(1580,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(1570,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
thf(1676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(1502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__mult__degree__sum_0) ).
thf(1751,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(1824,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(1619,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(2150,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
thf(2032,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(860,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
thf(2986,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(1920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(657,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(2477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(903,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(3090,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
thf(1888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(1457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(485,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(2068,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(536,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(2179,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_1) ).
thf(2345,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
thf(1195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(591,axiom,
( v_a____
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_kas_I1_J_0) ).
thf(2313,plain,
( v_a____
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(761,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(2741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(261,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__1_0) ).
thf(1573,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(977,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
thf(3271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(644,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(2445,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(943,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
thf(3191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(651,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(2464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(9,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(1032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(379,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1837,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(976,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_s____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_kas_I3_J_0) ).
thf(3269,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_s____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(733,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).
thf(2663,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(797,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(2826,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(795,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).
thf(2820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(987,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
thf(3297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(893,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(3065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(544,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(2200,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(711,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(2609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(926,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(3144,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(72,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(1159,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(286,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1634,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(1392,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(557,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(2228,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__single_0) ).
thf(1740,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_0) ).
thf(1910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(729,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
thf(2653,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(1106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(586,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
thf(2300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(444,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(1983,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
thf(1143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(823,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
thf(2895,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(803,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
thf(2841,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(743,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(2692,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(908,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
thf(3102,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(398,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
thf(1878,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(963,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(3237,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(50,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) ).
thf(1118,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(938,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(3176,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(1350,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(1936,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(665,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(2498,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(1541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(1762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(2100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(842,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(2946,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(862,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).
thf(2990,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(616,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(2377,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(786,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(2801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(1534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(2,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ofield )
| ( A @ tc_Polynomial_Opoly @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
thf(1017,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ofield )
| ( A @ tc_Polynomial_Opoly @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(855,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Omonom ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__monom_0) ).
thf(2973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Omonom ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(1121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(609,axiom,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_a00_0) ).
thf(2359,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(1375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(697,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_3) ).
thf(2577,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
thf(1064,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(1970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(744,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(2694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(1425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(755,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(2724,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__smult__left_0) ).
thf(1719,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(573,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(2268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(948,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_1) ).
thf(3205,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(950,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(3210,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(1461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(813,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(2868,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(870,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(3010,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(490,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
thf(2080,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(879,axiom,
( v_k____
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_kas_I2_J_0) ).
thf(3032,plain,
( v_k____
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(198,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
thf(1446,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(493,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2085,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(734,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(2666,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(777,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(2781,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(224,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
thf(1493,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(1683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(993,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(3311,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(816,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_1) ).
thf(2877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(435,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
thf(1964,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(1942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(866,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__mult__eq_0) ).
thf(3000,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(939,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(3179,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(2419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(1075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0_0) ).
thf(1414,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(477,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(2053,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(1842,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(944,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(3194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
thf(1612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(857,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
thf(2978,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(727,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(2649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(918,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(3126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(1668,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(607,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(2355,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1060,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(1947,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(792,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(2813,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(914,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(3115,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(811,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(2862,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1004,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(3333,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(1324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(668,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(2504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(2450,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(837,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= F )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(2932,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= F )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
thf(2125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(267,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
thf(1588,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(1539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(801,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( E @ ( A @ ( F @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
thf(2836,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( E @ ( A @ ( F @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
thf(1382,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(661,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__left_0) ).
thf(2487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(706,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(2598,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(890,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(3059,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Omonom ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0_0) ).
thf(1266,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Omonom ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(526,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(2153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(2387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(251,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
thf(1552,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(2243,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(693,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_0) ).
thf(2566,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
thf(1799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(476,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(2052,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(659,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__smult_0) ).
thf(2482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(745,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
thf(2697,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(911,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(3109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(442,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
thf(1979,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(897,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
thf(3074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(933,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(3162,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__0_0) ).
thf(1759,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
thf(1627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(953,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(3215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(927,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(3147,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(150,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
thf(1333,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(835,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(2926,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(958,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(3225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(2546,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(548,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(2208,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(472,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(2043,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(937,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(3173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(488,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
thf(2076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(209,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1466,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_1) ).
thf(2440,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(233,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
thf(1515,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(765,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd_0) ).
thf(2749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
thf(1857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(1991,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(780,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(2788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
thf(1202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(546,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(2203,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel_0) ).
thf(2057,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(991,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__smult__right_0) ).
thf(3306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(128,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
thf(1286,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(998,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(3321,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(613,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
thf(2368,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(1663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(496,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2089,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(1026,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(407,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
thf(1895,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(77,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(1167,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(2121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(1906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(293,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
thf(1648,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(451,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__mult__right_0) ).
thf(2001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(920,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(3130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(576,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
thf(2275,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
thf(1483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pCons_0) ).
thf(1273,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(840,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(2941,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(973,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(3262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
thf(1301,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(168,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
thf(1374,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(2524,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(738,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__left_0) ).
thf(2677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
thf(2176,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(1146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
thf(1754,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(583,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(2292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(826,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(2904,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(309,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
thf(1680,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(1959,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(2556,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(883,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(3042,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(701,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(2585,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(912,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
thf(3111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(978,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_0) ).
thf(3274,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(839,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
thf(2938,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(964,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(3240,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(806,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(2849,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__right_0) ).
thf(2188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(788,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__power_0) ).
thf(2806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
thf(1965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(1124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(516,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) ).
thf(2134,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(895,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(3070,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(756,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
thf(2727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(555,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mrmq__eq_0) ).
thf(2225,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(402,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
thf(1884,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(970,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(3255,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__neg_0) ).
thf(1652,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(1929,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(975,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(3266,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(737,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(2674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(672,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(2514,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(1795,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(625,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__right_0) ).
thf(2398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(1226,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(222,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( G @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( C @ ( F @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_1) ).
thf(1488,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( G @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( C @ ( F @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(848,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(2959,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(952,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(3213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(915,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(3118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(466,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(2029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(898,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(3077,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).
thf(1312,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(949,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(3208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1058,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(917,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( C @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__power_0) ).
thf(3123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( C @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(478,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
thf(2055,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(748,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
thf(2706,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(636,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( D @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( E @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult__less_0) ).
thf(2425,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( D @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( E @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(1258,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(990,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(3304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(655,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(2474,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(989,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(3302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(936,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(3170,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(1428,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(957,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(3223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(529,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(2161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1003,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__add_0) ).
thf(3330,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(760,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(2738,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(287,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(1635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(838,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(2935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1008,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(3340,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(531,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(2166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
thf(1765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(524,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(2148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(2319,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(670,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
thf(2510,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(590,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(2311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(126,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Ozero )
| ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
thf(1282,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Ozero )
| ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(724,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(2642,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(550,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(2214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(364,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(1806,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(983,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(3287,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(580,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(2284,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(910,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(3106,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(945,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
thf(3197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(814,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(2871,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(543,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(2197,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
thf(1209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(2721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(1013,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( D @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ ( E @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_0) ).
thf(3352,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( D @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ ( E @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(2538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult_0) ).
thf(1853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(2415,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(663,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_1) ).
thf(2493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(861,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(2987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(881,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(3038,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(635,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(2422,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(846,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(2955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(564,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(2246,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
thf(1722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(735,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(2669,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(508,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
thf(2116,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(802,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
thf(2839,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
thf(1690,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(940,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
thf(3182,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(303,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
thf(1667,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(955,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(3219,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(537,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(2182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(153,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( E @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( E @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
thf(1339,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( E @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( E @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(888,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(3055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(448,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
thf(1993,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(572,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(2267,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(570,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(2261,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(1162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(768,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(2757,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
thf(1952,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(463,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(2025,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(791,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(2812,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(32,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
thf(1080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(2129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(718,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
thf(2625,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(934,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(3165,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(1862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(630,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(2410,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(834,axiom,
! [B: $i,A: $i] :
( ( B
= ( t_a @ c_HOL_Ozero__class_Ozero ) )
| ( ( t_a @ ( B @ ( A @ c_Polynomial_Opoly ) ) )
= ( t_a @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2 )
!= ( t_a @ c_HOL_Ozero__class_Ozero ) )
| ~ ( t_a @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__decompose__lemma_0) ).
thf(2923,plain,
! [B: $i,A: $i] :
( ( B
= ( t_a @ c_HOL_Ozero__class_Ozero ) )
| ( ( t_a @ ( B @ ( A @ c_Polynomial_Opoly ) ) )
= ( t_a @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2 )
!= ( t_a @ c_HOL_Ozero__class_Ozero ) )
| ~ ( t_a @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(380,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1838,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(779,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(2785,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(704,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__one_0) ).
thf(2593,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(868,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(3006,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(815,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(2874,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(1556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(582,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(2289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(726,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(2647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1022,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(2252,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(1293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(577,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(2278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(750,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
thf(2710,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(829,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
thf(2911,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(371,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
thf(1820,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
thf(1171,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(773,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Oone__class_Oone ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(2770,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Oone__class_Oone ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(494,axiom,
tc_nat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(2086,plain,
tc_nat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(1643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(932,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(3159,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(681,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(2535,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(587,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(2303,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(1694,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(363,axiom,
tc_RealDef_Oreal @ class_HOL_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
thf(1805,plain,
tc_RealDef_Oreal @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(1562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__monom_0) ).
thf(1926,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(849,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(2962,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(611,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(2365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(214,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
thf(1474,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(604,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
thf(2350,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(626,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(2401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(549,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
thf(2212,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(2171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(15,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
thf(1044,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(26,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1066,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(716,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
thf(2620,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
thf(1113,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(784,axiom,
! [A: $i] :
( ( tc_Complex_Ocomplex @ ( A @ ( v_q____ @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_qr_0) ).
thf(2797,plain,
! [A: $i] :
( ( tc_Complex_Ocomplex @ ( A @ ( v_q____ @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(873,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_2) ).
thf(3016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
thf(1775,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(766,axiom,
! [B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_3) ).
thf(2752,plain,
! [B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(1435,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(721,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(2633,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0__iff_0) ).
thf(2022,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(1477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(925,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
thf(3142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(852,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( H @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( F @ ( E @ ( D @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( G @ ( A @ tc_Polynomial_Opoly @ ( F @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( E @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__mult_0) ).
thf(2967,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( H @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( F @ ( E @ ( D @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( G @ ( A @ tc_Polynomial_Opoly @ ( F @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( E @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(1250,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1034,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(1873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(210,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).
thf(1467,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(985,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(3293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
thf(2037,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__monom_0) ).
thf(1134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(1509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(545,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(2202,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
thf(1472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(980,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(3278,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(699,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(2582,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(1049,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(830,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(2914,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(366,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
thf(1809,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(844,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(2952,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(300,axiom,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(1662,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(713,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(2614,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(499,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
thf(2096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(76,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
thf(1166,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(504,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
thf(2107,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
thf(2333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(64,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(1145,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(805,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(2846,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(568,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(2256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(1845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(585,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(2298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1770,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(752,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(2715,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__pCons__0_0) ).
thf(1961,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(732,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(2661,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(70,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1156,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(900,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(3082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(522,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
thf(2143,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(702,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(2588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_1) ).
thf(1780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__add_0) ).
thf(2407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(242,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1531,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_0) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(818,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
thf(2882,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
thf(1547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).
thf(1748,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(234,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1516,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(271,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__def_0) ).
thf(1598,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(2060,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(1743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(758,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(2732,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(114,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).
thf(1252,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(165,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1368,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(959,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(3228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(799,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(2831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(742,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(2689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(354,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
thf(1785,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(877,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(3026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(552,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(2219,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(1901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(2599,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(152,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
thf(1336,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
thf(1711,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(874,axiom,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).
thf(3019,plain,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(899,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(3080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(764,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(2747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(227,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(1499,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(694,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(2569,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(966,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(3246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
thf(1790,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(327,axiom,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
thf(1716,plain,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(554,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(2224,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
thf(1813,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(1452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(288,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
thf(1637,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(913,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(3114,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(892,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(3063,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(2920,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(746,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(2700,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
thf(1085,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
thf(2322,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1002,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(3329,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(2044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(263,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(1579,plain,
tc_nat @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(882,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(3041,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(905,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(3095,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
thf(1934,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(507,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_1) ).
thf(2113,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(361,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1802,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(320,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
thf(1702,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
thf(1504,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(328,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(1717,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(931,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(3156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(700,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(2584,plain,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(1404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(161,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(1358,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
thf(1141,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
thf(1536,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(1981,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(1284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(431,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
thf(1955,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(2145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(220,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(1485,plain,
tc_nat @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(439,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
thf(1972,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(1052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(1506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(1797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(876,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mrmq__eq_1) ).
thf(3024,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(810,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(2860,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(843,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(2949,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(1372,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(971,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(3256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(822,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(2892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(658,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_Osmult ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
thf(2479,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_Osmult ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(206,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
thf(1459,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(794,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(2818,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(798,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(2828,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(1412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(99,axiom,
tc_nat @ class_OrderedGroup_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1216,plain,
tc_nat @ class_OrderedGroup_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(1126,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(45,axiom,
tc_nat @ class_HOL_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
thf(1108,plain,
tc_nat @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(1998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(812,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(2865,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(935,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_4) ).
thf(3168,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(640,axiom,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Complex_Oexpi )
= ( tc_Complex_Ocomplex @ ( B @ c_Complex_Oexpi @ ( A @ c_Complex_Oexpi @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_expi__add_0) ).
thf(2435,plain,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Complex_Oexpi )
= ( tc_Complex_Ocomplex @ ( B @ c_Complex_Oexpi @ ( A @ c_Complex_Oexpi @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(982,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Opoly ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset__poly_0) ).
thf(3284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Opoly ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(769,axiom,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(2760,plain,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(1421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(457,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(2013,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
thf(1839,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(924,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(3139,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__smult__left_0) ).
thf(1316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(1649,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(605,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
thf(2352,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
thf(1157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(489,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
thf(2078,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(1321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(1834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(415,axiom,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(1913,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(942,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(3188,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(2194,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(712,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(2611,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(595,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(2325,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(1448,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(662,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(2490,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(539,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(2187,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(506,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(2110,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(997,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(3320,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
thf(2342,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(2071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(731,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
thf(2658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(782,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(2792,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(1807,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(827,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(2907,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(643,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__is__one_1) ).
thf(2443,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(575,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(500,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(2098,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(517,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(2135,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(688,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(2554,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
thf(1481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1006,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
thf(3336,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(464,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
thf(2026,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(962,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(3235,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
thf(1523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(923,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__1_0) ).
thf(3136,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(677,axiom,
! [A: $i] :
( ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_s____ @ ( v_a____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_kas_I4_J_0) ).
thf(2526,plain,
! [A: $i] :
( ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_s____ @ ( v_a____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(254,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
thf(1558,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(1590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(534,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
thf(2174,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(621,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(2389,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(215,axiom,
tc_nat @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(1476,plain,
tc_nat @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(808,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(2855,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
thf(1639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(796,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(2823,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(956,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(3220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(790,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
thf(2811,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(1629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(909,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(3104,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(2004,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(867,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(3003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(771,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(2764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__cancel_0) ).
thf(1822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(623,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(2394,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(901,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(3085,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(841,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
thf(2944,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(455,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(2009,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
thf(1491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(313,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
thf(1689,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1000,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
thf(3324,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(2041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(1777,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(650,axiom,
( v_s____
= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(2462,plain,
( v_s____
= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(139,axiom,
tc_RealDef_Oreal @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
thf(1308,plain,
tc_RealDef_Oreal @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(140,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
thf(1309,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(196,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
thf(1442,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(776,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
thf(2779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__add_0) ).
thf(1614,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(195,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
thf(1440,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(597,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(2330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__offset__poly_0) ).
thf(1706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
thf(1193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(610,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(2362,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(739,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
thf(2680,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(502,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_1) ).
thf(2102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(1512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(1725,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(432,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
thf(1957,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(859,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(2983,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(1097,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(559,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
thf(2233,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(974,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(3264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(907,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(3100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(1876,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(921,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(3132,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(217,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
thf(1480,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(947,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(3203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
thf(1908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(521,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
thf(2142,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(511,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(2123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(569,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(2258,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(615,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(2374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__smult__right_0) ).
thf(2517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(2683,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(619,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( C @ ( B @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Opoly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset_1) ).
thf(2385,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( C @ ( B @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Opoly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(1678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(527,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__norm__inverse_0) ).
thf(2155,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(961,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
thf(3232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(1395,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(282,axiom,
! [A: $i] :
~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_1) ).
thf(1625,plain,
! [A: $i] :
~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
thf(1593,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(709,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(2604,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(793,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(2815,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(1986,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(454,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(2008,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(137,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__1_0) ).
thf(1303,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(1527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(66,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
thf(1148,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(390,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= D )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__poly__eq_0) ).
thf(1859,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= D )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(1989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(298,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= D )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__poly__eq_0) ).
thf(1657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= D )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(695,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(2572,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(2417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(783,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__power__ineq_0) ).
thf(2795,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(75,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
thf(1165,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(728,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).
thf(2651,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(686,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__linear__power_0) ).
thf(2549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(992,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(3309,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__linear__power_0) ).
thf(2636,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(1363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
thf(1314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
thf(1816,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).
thf(1495,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1011,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
thf(3347,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(979,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(3277,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(1288,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(1346,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(482,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
thf(2063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(276,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
thf(1610,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_1) ).
thf(1352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(1261,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(3,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(1019,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(652,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mult_0) ).
thf(2467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(972,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_0) ).
thf(3259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(1923,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(669,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(2507,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(325,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
thf(1713,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(1299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
thf(1885,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(574,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(2270,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(52,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1120,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(2138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(1093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(606,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
thf(2353,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__power_0) ).
thf(1236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(667,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(2502,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(562,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(2241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
thf(2127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(919,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_5) ).
thf(3128,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
thf(1829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(56,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
thf(1129,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(851,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
thf(2966,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(638,axiom,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(2430,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(889,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(3057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(243,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ofield )
| ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
thf(1532,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ofield )
| ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(824,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_0) ).
thf(2898,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(173,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
thf(1384,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(660,axiom,
( ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_Complex_Oexpi )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_expi__zero_0) ).
thf(2485,plain,
( ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_Complex_Oexpi )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(399,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(1880,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(191,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1431,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(872,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(3013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__neg__div_0) ).
thf(1606,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(767,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(2754,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(692,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(2563,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(336,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__0_0) ).
thf(1737,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(2018,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(185,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1416,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(417,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__0_0) ).
thf(1917,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(495,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(2087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(27,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1069,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(986,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(3296,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(730,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__lemma_0) ).
thf(2655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(1945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(951,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(3212,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(1681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(820,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(2887,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
thf(1184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(487,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( E @ ( D @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( A @ ( F @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( E @ ( B @ c_Polynomial_Osmult ) ) @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__smult__left_0) ).
thf(2074,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( E @ ( D @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( A @ ( F @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( E @ ( B @ c_Polynomial_Osmult ) ) @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
thf(1463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(865,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_realpow__num__eq__if_0) ).
thf(2998,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(1848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(480,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
thf(2059,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
thf(2238,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(647,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(2453,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(887,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__add__left_0) ).
thf(3052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(995,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(3316,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(800,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
thf(2834,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(1088,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(863,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__smult_0) ).
thf(2993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(946,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(3200,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(2191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
thf(1204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
thf(1468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(653,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(2470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(858,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__inverse_0) ).
thf(2980,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(880,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= C )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(3035,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= C )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1,negated_conjecture,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( v_w____ @ c_Power_Opower__class_Opower ) ) @ ( v_a____ @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1014,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( v_w____ @ c_Power_Opower__class_Opower ) ) @ ( v_a____ @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__iff_0) ).
thf(1870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(16409,plain,
$false,
inference(e,[status(thm)],[2163,2630,1586,1024,1767,1995,1559,2412,1031,1899,2559,2544,1179,2280,1686,3021,1665,2744,1369,2889,1168,2295,2306,3345,2336,3008,2109,2131,1454,1850,2499,2427,1083,1818,1295,1950,1549,1855,3185,1211,3072,1882,2644,3230,3153,1073,1269,2380,1793,1692,1437,1041,2309,2512,2976,1596,1406,2231,2622,2395,2908,1443,2776,2953,2590,1401,1569,1939,2671,1544,2014,1173,1486,1497,1671,1655,3120,3135,2918,1867,2141,2712,1233,1327,1342,2580,2844,2575,1788,3217,3049,1137,2607,2686,1756,1310,3044,1735,1164,2316,2448,3338,2476,2627,3253,2459,2901,3313,1095,3335,1746,2216,2020,3088,1645,2082,1366,1803,2957,2348,3350,2972,2046,2432,1914,2227,1576,1601,1386,3281,2067,1529,1967,2136,1904,1703,2531,2405,1228,1254,1287,1709,3029,2735,2039,3342,3061,2708,1330,3148,1826,1279,1191,1132,2703,3248,1409,2328,2916,1660,1298,2339,3046,2185,1455,2745,2356,2857,2767,1609,1398,1931,2158,1641,1773,2852,2533,1100,1847,1892,1379,2169,2403,1087,1247,2049,2552,1319,1890,1115,2929,2520,2730,2222,3322,2616,2090,2996,2782,1334,2880,1864,1828,1151,2254,2034,2017,2456,2007,1714,2027,2105,1811,1450,1109,1632,1418,2236,3290,3300,3093,2964,1896,1447,3327,2804,2762,2367,2437,3068,1377,2618,2281,2523,1072,1119,1622,2371,3243,2809,1345,2799,2286,2639,1104,1697,1242,2392,1521,2718,2205,1696,2884,1975,1564,1651,1604,2473,1306,1199,1153,2118,3318,1783,2773,3151,2011,3097,3011,1206,1470,2093,2083,2496,2790,1868,2382,1047,1730,2264,1223,1091,2601,2560,2249,1255,1217,2969,3250,2528,1883,1042,2541,1519,2596,1355,1580,1570,1676,1502,1751,1824,1619,2150,2032,2986,1423,1920,2477,3090,1888,1457,2068,2179,2345,1195,2313,2741,1291,1573,3271,2445,3191,2464,1032,1837,3269,2663,2826,2820,3297,3065,2200,2609,3144,1159,1634,1392,2228,1740,1910,2653,1106,2300,1983,1143,2895,2841,2692,3102,1878,3237,1118,3176,1350,1936,2498,1541,1762,2100,1270,2946,2990,2377,2801,1534,1017,2973,1121,2359,1375,2577,1064,1111,1970,2694,1425,2724,1719,2268,3205,1567,1028,1361,3210,1182,1461,2868,3010,2080,3032,1446,2085,2666,2781,1493,1683,3311,2877,1964,1942,3000,3179,2419,1075,1414,2053,1842,1214,3194,1612,2978,2649,1039,1263,3126,1668,2355,1060,1947,2813,3115,2862,3333,1324,2504,2450,2932,2125,1588,1539,2836,1382,2487,2598,3059,1266,2153,2387,1831,1552,2243,2566,1799,2052,2482,2697,3109,1979,3074,3162,1759,1627,3215,1525,3147,1333,2926,3225,2546,2208,2043,3173,2076,1466,2440,1515,1732,2749,1857,1991,2788,1202,2203,2057,3306,1054,1286,3321,2368,1663,2089,1026,1895,1167,2121,1906,1648,2001,1727,3130,2275,1219,1483,1273,2941,3262,1301,1374,2524,2677,2176,1146,1754,2292,2904,1680,1959,2556,3042,2585,3111,3274,2938,3240,2849,2188,2806,1965,1124,2134,3070,2727,2225,1884,1389,3255,1652,1929,3266,2674,2514,1795,2398,1226,1488,2959,3213,1139,3118,2029,3077,1312,3208,1058,3123,2055,2706,2425,1258,3304,2474,3302,3170,1428,3223,2161,3330,2738,1635,2935,3340,1239,2166,1765,2148,2319,2510,2311,1282,2642,2214,1806,3287,2284,3106,3197,2871,2197,2065,1209,2721,3352,2538,1853,2415,2493,2987,3038,2422,2955,2246,1722,2669,2116,2839,1690,3182,1667,3219,2182,1339,3055,1993,2267,2261,1162,2757,1952,2025,2812,1080,2129,2625,3165,1862,2410,2923,1838,2785,2593,3006,1149,2874,1556,2289,2647,1022,2252,1293,2278,2710,2911,1820,1171,2770,2086,1643,3159,1176,2535,2303,1102,1694,1805,1562,1926,2962,2365,1474,2350,2401,1699,2212,2171,1044,1245,1066,2620,1113,2797,3016,1775,2752,1435,2633,2022,1477,3142,2967,1250,1034,1873,1467,3293,2037,1134,1509,2202,1472,3278,2582,1049,2914,1583,1809,2952,1662,2614,2096,1166,2107,2333,1145,2846,2256,1845,2298,1770,2715,1961,2661,1156,3082,2143,2588,1780,2407,1531,1230,2882,1547,1748,1516,1598,2060,1743,2732,1252,1368,3228,2831,2689,1432,1785,3026,2219,1901,2599,1336,1711,3019,3080,2747,1499,2569,3246,1790,1716,2224,1813,1452,1637,3114,3063,2920,2700,1186,1085,2322,3329,2044,1130,1579,3041,3095,1934,2113,1802,1702,1504,1717,3156,2584,1617,1404,1358,1141,1536,1981,1221,1284,1955,2145,1485,1972,1052,1506,1797,3024,2860,2949,1372,3256,2892,2479,1459,2818,1553,2828,1412,1517,1216,1126,1108,1998,2865,3168,2435,3284,2760,1421,2013,1839,3139,1316,1649,2352,1157,2078,1321,1834,1913,3188,2194,2611,2325,1448,2490,2187,1189,2110,3320,2342,2071,2658,2792,1807,2907,2443,2273,2098,2135,2554,1062,1481,3336,2026,3235,1523,3136,2526,1558,1276,1590,2174,2389,1476,1674,2855,1639,2823,3220,2811,1629,3104,2004,3003,2764,1822,2394,3085,2944,2009,1491,1689,3324,2041,1777,2462,1308,1309,1442,2779,1045,1614,1440,2330,1706,1193,1077,2362,2680,1212,2102,1512,1725,1957,2983,1097,2233,3264,3100,1876,3132,1480,3203,1908,2142,2123,2258,2374,1348,2517,2683,2385,1678,2155,3232,1395,1625,1593,2604,2815,1986,2008,1303,1527,1148,1859,1989,1657,2572,2417,1056,2795,1165,2651,2549,3309,2636,1363,1314,1816,1495,3347,3277,1288,1197,1346,2063,1610,1352,1261,1019,2467,3259,1923,2507,1713,1299,1885,2270,1120,2138,1093,2353,1236,2502,2241,2127,3128,1829,1977,1129,2966,2430,3057,1532,2898,1384,2485,1880,1431,3013,1606,2754,2563,1737,2018,1416,1917,2087,1069,3296,2655,1945,3212,1681,2887,1184,2074,1463,2998,1848,2059,2238,1037,2453,3052,3316,2834,1088,2993,3200,2191,1204,1468,2470,2980,3035,1014,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG401-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/10.83 % Computer : n026.cluster.edu
% 0.16/10.83 % Model : x86_64 x86_64
% 0.16/10.83 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.83 % Memory : 8046.5625MB
% 0.16/10.83 % OS : Linux 6.8.0-71-generic
% 0.16/10.84 % CPULimit : 300
% 0.16/10.84 % WCLimit : 300
% 0.16/10.84 % DateTime : Sat Sep 26 22:00:51 UTC 2026
% 0.16/10.84 % CPUTime :
% 0.16/10.84 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.01/11.43 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.68/11.90 % [INFO] Parsing done (466ms).
% 2.68/11.92 % [INFO] Running in sequential loop mode.
% 3.60/12.33 % [INFO] eprover registered as external prover.
% 3.60/12.34 % [INFO] Scanning for conjecture ...
% 4.07/12.55 % [INFO] Found a conjecture (or negated_conjecture) and 1067 axioms. Running axiom selection ...
% 5.79/12.95 % [INFO] Axiom selection finished. Selected 1012 axioms (removed 55 axioms).
% 7.15/13.31 % [INFO] Problem is propositional (TPTP CNF).
% 7.15/13.35 % [INFO] Type checking passed.
% 7.15/13.35 % [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 ...
% 86.02/28.33 % External prover 'e' found a proof!
% 86.02/28.33 % [INFO] Killing All external provers ...
% 86.02/28.33 % Time passed: 17346ms (effective reasoning time: 16407ms)
% 86.02/28.35 % Axioms used in derivation (1012): cls_poly__decompose__lemma_0, cls_offset__poly__eq__0__iff_0, clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add, cls_degree__mult__eq_0, cls_add__0__left_0, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_power__0_0, cls_natgb_Oadd__r0__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, cls_neg__0__le__iff__le_1, cls_le__divide__eq_3, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add, cls_less__divide__eq_3, cls_not__one__less__zero_0, cls_poly__power_0, cls_mult__less__cancel__left__disj_5, cls_less__iff__diff__less__0_0, cls_real__mult__is__one_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oidom, cls_le__divide__eq_8, cls_dvd__div__neg_0, cls_minus__le__iff_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict, cls_pCons__0__0_0, cls_divide__eq__eq_3, cls_eq__add__iff2_1, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_mult__zero__right_0, cls_zero__less__one_0, cls_dvd__smult__iff_1, cls_divide__le__eq_2, cls_dvd__mult2_0, cls_DERIV__mult__lemma_0, cls_comm__semiring__class_Odistrib_0, cls_mod__mult__mult1_0, cls_smult__smult_0, cls_le__minus__self__iff_0, cls_divide__pos__pos_0, cls_smult__monom_0, cls_mult__imp__le__div__pos_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_dvd__mult__right_0, cls_degree__1_0, cls_smult__dvd__cancel_0, cls_divide__less__0__iff_0, clsarity_RealDef__Oreal__RealVector_Oreal__field, cls_offset__poly__pCons_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_zero__less__divide__iff_5, cls_inverse__zero__imp__zero_0, cls_divide__self_0, cls_pdivmod__rel__smult__right_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_left__minus_0, cls_square__eq__iff_1, cls_minus__zero_0, cls_power__eq__0__iff_1, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_mult_Odiff__left_0, cls_real__mult__assoc_0, cls_dvd__iff__poly__eq__0_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, cls_pdivmod__rel__def_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors, cls_real__less__def_1, cls_sum__squares__eq__zero__iff_0, cls_negative__imp__inverse__negative_0, cls_divide__nonpos__neg_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_Lim_Ominus__diff__minus_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1, cls_inverse__eq__iff__eq_0, cls_poly__offset_0, cls_mod__by__0_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_inverse__le__1__iff_2, cls_nonzero__inverse__eq__divide_0, cls_not__sum__squares__lt__zero_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_zero__le__divide__iff_2, cls_degree__smult__eq_1, cls_add__increasing2_0, cls_less__half__sum_0, cls_degree__pCons__0_0, cls_power__inject__exp_0, cls_mod__mod__cancel_0, cls_zero__le__mult__iff_3, clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add, cls_divide__1_0, cls_add__strict__right__mono_0, cls_CHAINED_0, cls_mult__poly__add__left_0, cls_power__le__zero__eq_3, cls_class__semiring_Osemiring__rules_I21_J_0, cls_div__add__self2_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_less__imp__inverse__less__neg_0, cls_add__is__0_0, cls_class__semiring_Osemiring__rules_I10_J_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_add__imp__eq_0, cls_divide__le__0__1__iff_1, cls_mod__add__left__eq_0, cls_nonzero__norm__inverse_0, cls_divide__le__eq_7, cls_minus__diff__eq_0, cls_inverse__less__1__iff_2, cls_add__le__cancel__right_1, cls_mod__add__eq_0, cls_divide__less__eq_4, cls_minus__add__distrib_0, cls_zero__less__divide__iff_0, cls_dvd__diff_0, cls_add__le__cancel__left_1, cls_divide__le__eq_8, cls_real__le__trans_0, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring, clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add, cls_div__smult__right_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, cls_frac__le_0, cls_a00_0, cls_dvd__div__mult__self_0, cls_poly__mult_0, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_one__le__inverse__iff_2, cls_poly__dvd__antisym_0, cls_inverse__1_0, cls_minus__le__self__iff_0, cls_minus__divide__right_0, cls_inverse__negative__iff__negative_1, cls_class__ringb_Onoteq__reduce_0, cls_minus__minus_0, cls_comm__monoid__add_Omult__assoc_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_divide__less__eq_5, cls_add__cancel__21_1, cls_mod__div__equality_0, cls_less__minus__iff_0, cls_mult__le__cancel__left__pos_0, cls_minus__dvd__iff_1, cls_divide__eq__eq_0, cls_mod__mult__self1__is__0_0, cls_mult__nonpos__nonpos_0, cls_class__ring_Osub__add_0, cls_mod__mult__right__eq_0, cls_comm__monoid__add_Omult__1__right_0, cls_sum__squares__ge__zero_0, cls_power__one_0, cls_add__nonpos__neg_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, clsarity_nat__HOL_Ozero, cls_mult__less__imp__less__right_0, cls_le__eq__neg_0, cls_left__inverse_0, cls_neg__less__iff__less_1, cls_mod__diff__eq_0, cls_pdivmod__rel_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_divide__le__0__iff_3, cls_mult__less__imp__less__left_0, cls_expi__add_0, cls_less__divide__eq_4, cls_coeff__1_1, cls_coeff__smult_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, cls_inverse__divide_0, cls_add__nonneg__pos_0, cls_smult__dvd__iff_2, cls_divide__strict__left__mono_0, cls_inverse__nonnegative__iff__nonnegative_0, cls_poly__monom_0, cls_div__by__0_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_lgqr_0, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0, cls_sum__squares__le__zero__iff_1, cls_mod__add__self2_0, clsarity_Polynomial__Opoly__Ring__and__Field_Odvd, cls_mult__less__cancel__right__disj_3, clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_eq__add__iff1_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, 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_divide__eq__eq_4, clsarity_nat__OrderedGroup_Omonoid__mult, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add, cls_norm__minus__commute_0, cls_coeff__monom_1, cls_double__add__less__zero__iff__single__less__zero_0, cls_add__right__mono_0, cls_dvd__iff__poly__eq__0_1, cls_norm__power__ineq_0, cls_divide__neg__neg_0, cls_eq__divide__eq_4, cls_mult__mono_0, cls_poly__add_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_mult__smult__right_0, cls_ab__left__minus_0, cls_mod__by__1_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_field__power__not__zero_0, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_neg__equal__iff__equal_0, cls_frac__eq__eq_0, clsarity_nat__Divides_Osemiring__div, cls_one__le__power_0, 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, cls_less__add__iff2_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_mult_Ozero__left_0, cls_smult__eq__0__iff_1, cls_less__iff__diff__less__0_1, cls_mod__minus__eq_0, cls_inverse__le__1__iff_1, 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, clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult, cls_double__eq__0__iff_1, clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, cls_div__poly__eq_0, 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_dvd__neg__div_0, cls_mult__pos__neg_0, cls_div__mult__self2__is__id_0, cls_inverse__eq__1__iff_1, cls_mult__strict__mono_0, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1, cls_mult_Ozero__right_0, cls_inverse__minus__eq_0, cls_mult__left__mono_0, cls_divide__strict__left__mono__neg_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, cls_right__minus__eq_0, cls_mult__dvd__mono_0, cls_mult_Oadd__left_0, cls_div__self_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_class__fieldgb_Oinverse__divide_0, cls_neg__0__le__iff__le_0, cls_divide__left__mono__neg_0, cls_inverse__nonzero__iff__nonzero_0, cls_less__divide__eq_7, cls_add__cancel__end_0, cls_div__mult__mult1_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_norm__one_0, cls_minus__less__iff_1, cls_power__le__zero__eq_0, cls_mod__div__trivial_0, cls_power__one__over_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_dvd__mult__cancel__right_2, cls_inverse__nonpositive__iff__nonpositive_0, cls_inverse__nonnegative__iff__nonnegative_1, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add, cls_mult__pCons__left_0, cls_mult__right_Oadd_0, cls_minus__add__cancel_0, cls_real__less__def_0, cls_dvd__mult__div__cancel_0, cls_le__divide__eq_7, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_add__nonneg__eq__0__iff_0, cls_le__divide__eq_2, cls_add__less__cancel__right_1, cls_neg__less__eq__nonneg_0, cls_divide__le__eq_3, cls_mod__mult__self1_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_degree__0_0, cls_no__zero__divisors_0, cls_mult__frac__num_0, cls_neg__less__eq__nonneg_1, cls_zero__le__double__add__iff__zero__le__single__add_1, clsarity_Polynomial__Opoly__HOL_Ozero, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_divide__neg__pos_0, cls_mult__monom_0, cls_mod__add__cong_0, cls_coeff__0_0, cls_add__left__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero, cls_le__minus__iff_0, cls_nat__add__left__commute_0, cls_add__divide__distrib_0, cls_degree__smult__eq_0, cls_div__mult__div__if__dvd_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, cls_zero__le__mult__iff_4, cls_power__gt1__lemma_0, cls_divide__less__eq_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_div__add__self1_0, cls_class__semiring_Osemiring__rules_I2_J_0, cls_mult__1__right_0, cls_add__strict__left__mono_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_dvd__imp__mod__0_0, cls_less__divide__eq_2, cls_mod__smult__right_0, cls_mod__div__equality2_0, cls_zero__less__divide__iff_1, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult, cls_mult__frac__frac_0, cls_leading__coeff__0__iff_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_CHAINED_0_01, cls_poly__eq__0__iff__dvd_1, cls_cq0_0, cls_inverse__le__imp__le__neg_0, cls_mult__le__0__iff_0, cls_add__le__less__mono_0, cls_le__iff__diff__le__0_0, cls_real__le__refl_0, cls_mod__minus__cong_0, cls_mult__neg__pos_0, cls_poly__offset_1, cls_norm__power_0, cls_combine__common__factor_0, cls_pCons__eq__0__iff_1, cls_mult__left_Odiff_0, cls_less__add__iff1_0, cls_mult__right__le__imp__le_0, cls_pCons__eq__iff_0, cls_power__eq__0__iff_2, cls_diff__minus_0, cls_monom__0_0, cls_div__mod__equality2_0, cls_dvd__mod__iff_1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add, cls_neg__le__0__iff__le_0, cls_inf__period_I4_J_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add, cls_mult__pos__neg2_0, cls_pdivmod__rel__by__0_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__mono1_0, cls_mult__less__cancel__left__disj_0, cls_dvd__trans_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_mod__mult__left__eq_0, cls_zero__le__divide__iff_3, cls_le__imp__inverse__le_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, cls_class__ringb_Onoteq__reduce_1, cls_le__eq__neg_1, cls_le__add__iff1_1, cls_class__semiring_Osemiring__rules_I19_J_0, cls_mult__le__cancel__left__neg_1, cls_div__mult__self1_0, cls_smult__0__left_0, cls_class__semiring_Oadd__0_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, cls_mod__smult__left_0, cls_diff__def_0, cls_eq__divide__eq_0, cls_mult_Odiff__right_0, clsarity_nat__Ring__and__Field_Opordered__cancel__semiring, cls_dvd__minus__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1, cls_mult__le__cancel__left__pos_1, cls_one__le__inverse__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, cls_less__add__iff2_1, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add, cls_coeff__1_0, cls_zero__less__mult__pos_0, cls_divide__self__if_1, cls_mult__le__0__iff_1, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add, cls_class__semiring_Osemiring__rules_I1_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_eq__divide__eq_3, cls_inverse__negative__imp__negative_0, cls_split__mult__pos__le_0, cls_sum__squares__le__zero__iff_2, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring, cls_divide_Ozero_0, cls_divide__self__if_0, clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add, cls_zero__le__power__iff_1, cls_class__semiring_Osemiring__rules_I17_J_0, clsarity_Polynomial__Opoly__Divides_Osemiring__div, cls_power__less__power__Suc_0, cls_mult__imp__div__pos__le_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, clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors, cls_mult_Ominus__right_0, cls_add__strict__mono_0, cls_neg__0__less__iff__less_0, cls_pdivmod__rel__def_3, cls_neg__less__0__iff__less_0, cls_nonzero__minus__divide__right_0, clsarity_nat__Ring__and__Field_Omult__mono, cls_zero__le__divide__iff_5, clsarity_RealDef__Oreal__Ring__and__Field_Oring__1, cls_mult__le__0__iff_4, cls_le__minus__self__iff_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict, cls_smult__1__left_0, cls_dvd__triv__right_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, cls_less__add__one_0, cls_class__ringb_Oadd__mul__solve_0, cls_degree__linear__power_0, cls_coeff__mult__degree__sum_0, cls_sum__squares__eq__zero__iff_1, cls_neg__equal__0__iff__equal_0, cls_divide__less__0__iff_3, cls_mult__less__cancel__right__disj_2, cls_zero__less__power_0, cls_minus__le__self__iff_1, cls_pdivmod__rel__mult_0, cls_divide__le__eq_6, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_dvd__add_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, cls_power__divide_0, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_divide__le__0__iff_2, cls_zero__less__power__eq_3, cls_pdivmod__rel__by__0__iff_0, cls_dvd__div__mult_0, cls_divide__less__eq_8, cls_offset__poly__eq__0__lemma_0, cls_coeff__monom_0, cls_qr_0, cls_add__cancel__21_0, cls_nonzero__inverse__minus__eq_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_eq__add__iff1_1, cls_smult__dvd__iff_1, cls_divide__nonneg__neg_0, cls_divide__less__eq_1, cls_mult__left__less__imp__less_0, cls_ab__diff__minus_0, cls_class__semiring_Omul__d_0, cls_monom__eq__0__iff_0, cls_neg__equal__zero_1, cls_Deriv_Oinverse__diff__inverse_0, clsarity_Polynomial__Opoly__Divides_Oring__div, cls_no__zero__divirors__neq0_0, cls_poly__mod__mult__right_0, cls_inverse__le__1__iff_0, cls_mult__le__0__iff_5, cls_mult__strict__mono_H_0, cls_one__poly__def_0, cls_mod__diff__cong_0, cls_zero__neq__one_0, cls_group__add__class_Odiff__0_0, cls_poly__0_0, cls_less__divide__eq_5, cls_class__semiring_Osemiring__rules_I5_J_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one, clsarity_Polynomial__Opoly__Power_Opower, cls_split__mult__pos__le_1, cls_mod__mult__cong_0, cls_add__frac__eq_0, cls_inverse__nonzero__iff__nonzero_1, cls_dvd__mult__cancel__left_2, cls_mult__pCons__right_0, cls_less__divide__eq_8, cls_divide__le__eq_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict, cls_mult__right_Ominus_0, cls_mod__poly__eq_0, cls_div__by__1_0, cls_diff__self_0, cls_dvd__smult__cancel_0, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add, cls_inverse__add_0, cls_natgb_Oadd__cancel_0, cls_zero__less__divide__iff_3, cls_mult__poly__0__left_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector, cls_realpow__num__eq__if_0, cls_add__num__frac_0, cls_mult__smult__left_0, cls_zero__le__divide__iff_4, cls_le__add__iff2_1, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_smult__add__left_0, cls_dvd__refl_0, cls_inverse__eq__1__iff_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring, cls_dvd__mult__cancel__right_1, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add, cls_pdivmod__rel__def_6, cls_divide__le__0__iff_5, cls_less__1__mult_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, cls_less__imp__inverse__less_0, cls_divide__nonneg__pos_0, cls_minus__less__iff_0, cls_mod__mult__self2_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add, cls_add__diff__cancel_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult, cls_add__less__cancel__right_0, cls_divide__zero_0, cls_leading__coeff__0__iff_1, cls_mult__less__cancel__right__disj_5, cls_kas_I4_J_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one, cls_inverse__less__1__iff_0, clsarity_RealDef__Oreal__HOL_Ozero, cls_right__inverse_0, cls_divide__le__eq_4, cls_class__semiring_Omul__a_0, cls_zero__le__square_0, cls_equation__minus__iff_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_kas_I1_J_0, cls_add__increasing_0, cls_poly__eq__0__iff__dvd_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero, clsarity_nat__Ring__and__Field_Odvd, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, cls_synthetic__div__unique_0, cls_neg__0__equal__iff__equal_1, cls_le__add__iff1_0, cls_power__inverse_0, cls_less__eq__neg__nonpos_1, cls_inverse__positive__iff__positive_0, cls_less__minus__iff_1, cls_inf__period_I4_J_1, cls_class__semiring_Omul__1_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_kas_I3_J_0, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring, cls_dvd__mod_0, cls_mult__nonneg__nonpos_0, cls_inverse__positive__iff__positive_1, cls_class__ringb_Oadd__scale__eq__noteq_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_less__divide__eq_1, cls_inverse__unique_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add, cls_div__mod__equality_0, cls_le__divide__eq_6, cls_mrmq__eq_1, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1, cls_class__ringb_Oadd__cancel_0, cls_add__nonneg__eq__0__iff_1, cls_le__divide__eq_1, cls_divide__le__0__iff_1, cls_zero__less__divide__iff_2, cls_right__minus__eq_1, 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, cls_less__add__iff1_1, cls_mult__imp__less__div__pos_0, cls_diff__minus__eq__add_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono, cls_le__divide__eq_0, cls_divide__zero__left_0, cls_linorder__neqE__ordered__idom_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_div__dvd__div_0, cls_div__add_0, cls_mod__diff__right__eq_0, cls_dvd__triv__left_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1, cls_mult__left__le__one__le_0, cls_add__nonpos__nonpos_0, cls_divide__pos__neg_0, cls_one__less__inverse__iff_2, cls_mod__add__self1_0, clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring, clsarity_Complex__Ocomplex__Ring__and__Field_Oring, cls_mod__0_0, cls_class__semiring_Osemiring__rules_I3_J_0, cls_one__le__inverse__iff_0, cls_mult__eq__0__iff_2, cls_pdivmod__rel__0_0, cls_add__nonneg__nonneg_0, cls_class__ring_Oneg__mul_0, cls_neg__le__0__iff__le_1, cls_smult__dvd__iff_3, cls_mult__strict__left__mono__comm_0, cls_pdivmod__rel__0__iff_1, cls_sum__squares__gt__zero__iff_1, cls_eq__divide__eq_2, clsarity_nat__Ring__and__Field_Osemiring, cls_eq__neg__iff__add__eq__0_1, cls_mult__mono_H_0, cls_complex__divide__def_0, cls_mod__mod__trivial_0, cls_pdivmod__rel__by__0__iff_1, cls_class__ringb_Oadd__r0__iff_0, cls_norm__inverse_0, cls_add__pCons_0, cls_mult__less__cancel__left__neg_1, cls_dvd__minus__iff_0, cls_divide_Odiff_0, cls_psize__eq__0__iff_0, cls_division__ring__inverse__add_0, cls_poly__div__mult__right_0, cls_even__less__0__iff_1, cls_add__strict__increasing_0, cls_dvd__power_1, cls_one__dvd_0, cls_le__imp__neg__le_0, clsarity_nat__Power_Opower, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring, cls_smult__add__right_0, cls_div__0_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odvd, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add, cls_divide__strict__right__mono__neg_0, cls_mult__less__cancel__left__pos_1, cls_divide__less__eq_2, cls_dvd__mod__iff_0, cls_minus__divide__divide_0, cls_divide__less__0__1__iff_0, cls_zero__le__mult__iff_5, cls_divide__le__eq_5, cls_kas_I2_J_0, cls_inverse__negative__iff__negative_0, cls_nonzero__inverse__inverse__eq_0, cls_CHAINED_0_02, 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cls_mult__imp__div__pos__less_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_mod__mult__self2__is__0_0, cls_neg__less__0__iff__less_1, cls_real__le__antisym_0, cls_diff__0__right_0, cls_div__mult__self2_0, cls_pCons__eq__0__iff_0, cls_zero__less__mult__pos2_0, cls_pCons__eq__iff_1, cls_divide__less__0__iff_5, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring, cls_zmod__simps_I2_J_0, cls_dvd__mult__left_0, cls_mod__add__right__eq_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, cls_zero__less__power__eq_2, cls_comm__monoid__add_Omult__left__commute_0, cls_add__frac__num_0, cls_mult__right__mono__neg_0, cls_neg__equal__zero_0, cls_sum__squares__eq__zero__iff_2, cls_diff__divide__distrib_0, cls_add__minus__cancel_0, cls_div__power_0, clsarity_RealDef__Oreal__Ring__and__Field_Odvd, cls_divide__less__0__iff_2, cls_positive__imp__inverse__positive_0, cls_le__add__right__mono_0, 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clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add, cls_monoid__add__class_Oadd__0__right_0, cls_mult__idem_0, cls_dvd__mult_0, cls_le__imp__inverse__le__neg_0, cls_div__mult__mult1__if_0, cls_norm__minus__cancel_0, cls_add__strict__increasing2_0, clsarity_RealDef__Oreal__Int_Onumber__ring, cls_div__smult__left_0, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_semiring__div__class_Omod__div__equality_H_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict, cls_eq__iff__diff__eq__0_0, cls_mult__le__0__iff_3, cls_inverse__nonpositive__iff__nonpositive_1, cls_mult__neg__neg_0, cls_divide_Ominus_0, cls_mult__less__le__imp__less_0, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_divide__less__0__1__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1, cls_power__Suc__less_0, cls_poly__1_0, cls_square__eq__iff_0, cls_zero__less__divide__1__iff_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_le__add__iff2_0, cls_not__one__le__zero_0, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, cls_mod__self_0, cls_less__eqI_1, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_neg__less__iff__less_0, cls_power__0__left_1, cls_sum__squares__le__zero__iff_0, cls_mult__less__cancel__left__pos_0, cls_split__mult__neg__le_1, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, cls_power__mono_0, cls_divide__le__eq_1, cls_divide__le__0__1__iff_0, cls_coeff__add_0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_even__less__0__iff_0, cls_offset__poly__single_0, cls_mult__left_Oadd_0, cls_add__le__cancel__right_0, cls_mult__right_Odiff_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0, cls_dvd__eq__mod__eq__0_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, clsarity_Complex__Ocomplex__HOL_Ozero, cls_dvd__smult__iff_0, cls_divide__less__0__iff_4, cls_nat__add__commute_0, cls_Deriv_Oadd__diff__add_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Osemiring__rules_I22_J_0, cls_poly__offset__poly_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict, cls_right__inverse__eq_1, cls_zero__le__mult__iff_2, cls_dvd__0__left_0
% 86.02/28.35 % No. of inferences in proof: 2027
% 86.02/28.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 17346 ms resp. 16407 ms w/o parsing
% 88.49/28.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 88.49/28.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------