%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG380-1 : 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 : n009.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 06:46:48 AM UTC 2026
% Result : Unsatisfiable 32.85s 8.42s
% Output : Refutation 36.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1216
% Syntax : Number of formulae : 2433 ( 639 unt; 0 typ; 0 def)
% Number of atoms : 7083 (1244 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 39254 (4252 ~;4650 |; 0 &;30352 @)
% ( 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; 10 con; 0-3 aty)
% Number of variables : 5548 ( 0 ^;5548 !; 0 ?;5548 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Complex_Orcis_decl,type,
c_Complex_Orcis: $i > $i > $i ).
thf(c_NthRoot_Osqrt_decl,type,
c_NthRoot_Osqrt: $i > $i ).
thf(c_HOL_Oabs__class_Oabs_decl,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(v_r_decl,type,
v_r: $i ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(c_HOL_Oinverse__class_Odivide_decl,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(v_a_decl,type,
v_a: $i ).
thf(c_Int_Onumber__class_Onumber__of_decl,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(c_Int_OBit0_decl,type,
c_Int_OBit0: $i > $i ).
thf(c_Int_OBit1_decl,type,
c_Int_OBit1: $i > $i ).
thf(c_Int_OPls_decl,type,
c_Int_OPls: $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $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_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_Int_Onumber_decl,type,
class_Int_Onumber: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_Transcendental_Ocos_decl,type,
c_Transcendental_Ocos: $i > $i ).
thf(c_Transcendental_Osin_decl,type,
c_Transcendental_Osin: $i > $i ).
thf(c_HOL_Oinverse__class_Oinverse_decl,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_decl,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(class_RealVector_Oreal__algebra__1_decl,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
thf(c_RealVector_Oof__real_decl,type,
c_RealVector_Oof__real: $i > $i > $i ).
thf(class_HOL_Oeq_decl,type,
class_HOL_Oeq: $i > $o ).
thf(c_HOL_Oeq__class_Oeq_decl,type,
c_HOL_Oeq__class_Oeq: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(c_RealVector_Onorm__class_Onorm_decl,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(c_HOL_Osgn__class_Osgn_decl,type,
c_HOL_Osgn__class_Osgn: $i > $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(c_Transcendental_Opi_decl,type,
c_Transcendental_Opi: $i ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $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_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add__abs_decl,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $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_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_Ring__and__Field_Odivision__ring_decl,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(c_Transcendental_Otan_decl,type,
c_Transcendental_Otan: $i > $i ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1_decl,type,
c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1: $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Int_Oiszero_decl,type,
c_Int_Oiszero: $i > $i > $o ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $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_Ono__zero__divisors_decl,type,
class_Ring__and__Field_Ono__zero__divisors: $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_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_Ring__and__Field_Osgn__if_decl,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
thf(class_Ring__and__Field_Olordered__ring_decl,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_decl,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_decl,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(class_Ring__and__Field_Oabs__if_decl,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
class_RealVector_Oreal__normed__algebra__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_Omult__mono_decl,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_Int_Oring__char__0_decl,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring__abs_decl,type,
class_Ring__and__Field_Opordered__ring__abs: $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_RealVector_Oreal__normed__div__algebra_decl,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(c_Complex_Ocis_decl,type,
c_Complex_Ocis: $i > $i ).
thf(class_RealVector_Oreal__field_decl,type,
class_RealVector_Oreal__field: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(729,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(2822,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_9) ).
thf(1501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(229,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(1718,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)],[229]) ).
thf(88,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(1411,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)],[88]) ).
thf(710,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(2778,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)],[710]) ).
thf(355,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
thf(1995,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1201,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(3798,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)],[1201]) ).
thf(1020,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_1) ).
thf(3434,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(540,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(2412,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)],[540]) ).
thf(566,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(2463,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)],[566]) ).
thf(284,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(1840,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)],[284]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
thf(2427,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(1028,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
thf(3449,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(605,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
thf(2544,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1084,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).
thf(3566,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(38,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(1295,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)],[38]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__square__gt__zero_0) ).
thf(1549,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(469,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(2250,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)],[469]) ).
thf(444,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
= ( A @ c_Transcendental_Otan ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic__pi_0) ).
thf(2199,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
= ( A @ c_Transcendental_Otan ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(821,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__diff_0) ).
thf(3021,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(50,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(1322,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)],[50]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
thf(1665,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(633,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).
thf(2612,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(114,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1469,plain,
tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(695,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_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_1) ).
thf(2744,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_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(70,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(1369,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)],[70]) ).
thf(488,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(2295,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)],[488]) ).
thf(492,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(2306,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(978,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(3345,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)],[978]) ).
thf(508,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(2341,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)],[508]) ).
thf(814,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
= ( A @ c_Transcendental_Otan ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic__n_0) ).
thf(3008,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
= ( A @ c_Transcendental_Otan ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(2109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(415,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(2131,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)],[415]) ).
thf(108,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(1454,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)],[108]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(2031,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(391,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(2072,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)],[391]) ).
thf(252,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(1767,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)],[252]) ).
thf(1132,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(3666,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)],[1132]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_2) ).
thf(1729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(774,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(2921,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)],[774]) ).
thf(1043,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(3477,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)],[1043]) ).
thf(1150,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).
thf(3698,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(47,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(1315,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)],[47]) ).
thf(288,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(1850,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)],[288]) ).
thf(1140,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(3680,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)],[1140]) ).
thf(966,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_1) ).
thf(3317,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(36,axiom,
~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( c_Transcendental_Opi @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__not__less__zero_0) ).
thf(1290,plain,
~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( c_Transcendental_Opi @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(638,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(2622,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)],[638]) ).
thf(948,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).
thf(3285,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(831,axiom,
! [C: $i,B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_realpow__two__le__add__order2_0) ).
thf(3040,plain,
! [C: $i,B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(659,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(2671,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)],[659]) ).
thf(816,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__x__y__le__one_0) ).
thf(3012,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_9) ).
thf(1591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(737,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(2837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1006,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
thf(3402,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_1) ).
thf(1305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(998,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(3382,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)],[998]) ).
thf(122,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(1486,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)],[122]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ 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_Rational_Oordered__idom__class_Osgn__less_0) ).
thf(1750,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ 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)],[243]) ).
thf(898,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(3185,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)],[898]) ).
thf(494,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(2309,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)],[494]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(2512,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(800,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ 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_abs__less__iff_0) ).
thf(2976,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ 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)],[800]) ).
thf(847,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
thf(3072,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Int_Oiszero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__def_0) ).
thf(1924,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Int_Oiszero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(449,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(2210,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)],[449]) ).
thf(783,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(2940,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)],[783]) ).
thf(86,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(1406,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)],[86]) ).
thf(1208,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(3813,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_0) ).
thf(2381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(769,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(2908,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)],[769]) ).
thf(387,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(2062,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)],[387]) ).
thf(103,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(1443,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)],[103]) ).
thf(270,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(1808,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)],[270]) ).
thf(653,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(2659,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)],[653]) ).
thf(789,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(2953,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(84,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(1401,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)],[84]) ).
thf(93,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(1422,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)],[93]) ).
thf(161,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(1569,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)],[161]) ).
thf(468,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(2248,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)],[468]) ).
thf(819,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__sum_0) ).
thf(3017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1067,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(3530,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)],[1067]) ).
thf(208,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(1671,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)],[208]) ).
thf(1023,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_1) ).
thf(3439,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1017,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
thf(3429,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1122,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(3648,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__mult_0) ).
thf(3044,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(893,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(3175,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(558,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
thf(2448,plain,
tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(1191,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__pow2__gt__zero_0) ).
thf(3781,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(52,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(1327,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)],[52]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(1761,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(964,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult__self__sum__ge__zero_0) ).
thf(3313,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(740,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(2844,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)],[740]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_7) ).
thf(1354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(943,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__gt__zero_0) ).
thf(3276,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(835,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).
thf(3049,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1175,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(3745,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(246,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(1756,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)],[246]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_9) ).
thf(1310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(875,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ( A @ ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_1) ).
thf(3135,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ( A @ ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1123,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__ge1_0) ).
thf(3649,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(989,axiom,
( ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Transcendental_Ocos )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__neq__zero_0) ).
thf(3365,plain,
( ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Transcendental_Ocos )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(693,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(2740,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(773,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(2918,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)],[773]) ).
thf(28,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(1275,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)],[28]) ).
thf(419,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(2141,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)],[419]) ).
thf(551,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
thf(2434,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(298,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(1872,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)],[298]) ).
thf(1107,axiom,
! [A: $i] :
( ( A = c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_lessequals ) ) )
| ( ( A @ c_Transcendental_Ocos )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__is__zero_3) ).
thf(3616,plain,
! [A: $i] :
( ( A = c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_lessequals ) ) )
| ( ( A @ c_Transcendental_Ocos )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
thf(1233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(640,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(2627,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)],[640]) ).
thf(22,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(1260,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)],[22]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
thf(1919,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(563,axiom,
tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
thf(2459,plain,
tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1088,axiom,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
thf(3577,plain,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(2042,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(133,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(1507,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)],[133]) ).
thf(3,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(1222,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)],[3]) ).
thf(1159,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__le__two_0) ).
thf(3717,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(862,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__divide_0) ).
thf(3103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_RealVector_Oof__real ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__of__real_0) ).
thf(1835,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_RealVector_Oof__real ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_0) ).
thf(2216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(1189,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(3777,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(198,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(1650,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)],[198]) ).
thf(433,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(2173,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(592,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
thf(2516,plain,
tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(599,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(2531,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
thf(1887,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(791,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(2957,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(980,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__is__zero_1) ).
thf(3350,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1074,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
thf(3545,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(686,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(2723,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)],[686]) ).
thf(550,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(2432,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)],[550]) ).
thf(318,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(1914,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)],[318]) ).
thf(13,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(1243,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)],[13]) ).
thf(703,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(2763,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)],[703]) ).
thf(804,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
thf(2985,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(457,axiom,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__zero_0) ).
thf(2227,plain,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(165,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(1576,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)],[165]) ).
thf(929,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__double_0) ).
thf(3249,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(102,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(1441,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)],[102]) ).
thf(367,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(2020,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)],[367]) ).
thf(1059,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(3513,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)],[1059]) ).
thf(759,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
thf(2886,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(878,axiom,
( c_Int_OPls
= ( c_Int_OPls @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I38_J_1) ).
thf(3140,plain,
( c_Int_OPls
= ( c_Int_OPls @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(231,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(1724,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)],[231]) ).
thf(389,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Int_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__0_0) ).
thf(2067,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Int_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(145,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(1529,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)],[145]) ).
thf(417,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(2136,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)],[417]) ).
thf(313,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
thf(1904,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(138,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
thf(1518,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(24,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(1265,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)],[24]) ).
thf(120,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(1482,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)],[120]) ).
thf(19,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(1254,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)],[19]) ).
thf(1144,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_1) ).
thf(3688,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(752,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(2869,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)],[752]) ).
thf(87,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(1409,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)],[87]) ).
thf(915,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_four__x__squared_0) ).
thf(3221,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
thf(1709,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(630,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(2603,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)],[630]) ).
thf(263,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(1792,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)],[263]) ).
thf(942,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(3275,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(657,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(2667,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)],[657]) ).
thf(700,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_1) ).
thf(2755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1213,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(3821,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(1125,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__iszero__Numeral1_0) ).
thf(3653,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1046,axiom,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
thf(3485,plain,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oeq__class_Oeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I16_J_0) ).
thf(1279,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oeq__class_Oeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(764,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
thf(2897,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(111,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_3) ).
thf(1462,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(651,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(2654,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)],[651]) ).
thf(189,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(1628,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)],[189]) ).
thf(904,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(3195,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(826,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).
thf(3029,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(691,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(2735,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(726,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__diff_0) ).
thf(2814,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(350,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(1985,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)],[350]) ).
thf(248,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oabs__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).
thf(1760,plain,
tc_Int_Oint @ class_Ring__and__Field_Oabs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(203,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(1660,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)],[203]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(1298,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(665,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(2682,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)],[665]) ).
thf(872,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).
thf(3125,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(438,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(2185,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)],[438]) ).
thf(945,axiom,
! [A: $i] :
( ( A @ c_Complex_Ocis )
= ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_Complex_Orcis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cis__rcis__eq_0) ).
thf(3280,plain,
! [A: $i] :
( ( A @ c_Complex_Ocis )
= ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_Complex_Orcis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(612,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
thf(2562,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(855,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
thf(3089,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(567,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(2466,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)],[567]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_0) ).
thf(2126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(321,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(1922,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)],[321]) ).
thf(681,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(2713,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)],[681]) ).
thf(608,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(2552,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)],[608]) ).
thf(222,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(1704,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)],[222]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_RealVector_Oof__real ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
thf(1609,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_RealVector_Oof__real ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_1) ).
thf(2373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(1040,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(3470,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)],[1040]) ).
thf(689,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(2730,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)],[689]) ).
thf(806,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(2989,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)],[806]) ).
thf(300,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(1875,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)],[300]) ).
thf(600,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(2533,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)],[600]) ).
thf(934,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).
thf(3258,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(287,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(1847,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)],[287]) ).
thf(1194,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__pi__half_0) ).
thf(3788,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(1545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(544,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(2420,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)],[544]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_9) ).
thf(1892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(74,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(1379,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)],[74]) ).
thf(999,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(3385,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)],[999]) ).
thf(431,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(2169,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)],[431]) ).
thf(1118,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__power2_0) ).
thf(3638,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(136,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(1514,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oeq__class_Oeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I16_J_1) ).
thf(1741,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oeq__class_Oeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(852,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__sin__le__one_0) ).
thf(3084,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(963,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(3312,plain,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(160,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1568,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1127,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_1) ).
thf(3657,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(325,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(1931,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)],[325]) ).
thf(194,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(1641,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)],[194]) ).
thf(1155,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__squared__add2__mult_0) ).
thf(3708,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(490,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
thf(2301,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(126,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(1494,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)],[126]) ).
thf(562,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(2456,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)],[562]) ).
thf(968,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__gt__zero_0) ).
thf(3322,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1065,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__norm__divide_0) ).
thf(3524,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_2) ).
thf(1714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(906,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__abs1_0) ).
thf(3199,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1002,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__30_0) ).
thf(3393,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(955,axiom,
! [A: $i] :
( ( A = c_Int_OPls )
| ( ( A @ c_Int_OBit0 )
!= c_Int_OPls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I44_J_0) ).
thf(3295,plain,
! [A: $i] :
( ( A = c_Int_OPls )
| ( ( A @ c_Int_OBit0 )
!= c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(762,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2893,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(756,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(2880,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)],[756]) ).
thf(1186,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__less__0_0) ).
thf(3771,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__times_0) ).
thf(2017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(788,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(2950,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)],[788]) ).
thf(462,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(2237,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)],[462]) ).
thf(41,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(1302,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)],[41]) ).
thf(717,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(2794,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)],[717]) ).
thf(404,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(2105,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)],[404]) ).
thf(848,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(3075,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( 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__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_0) ).
thf(1811,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( 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__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(106,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_4) ).
thf(1450,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1134,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( B @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( B @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__diff2_0) ).
thf(3670,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( B @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( B @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(473,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(2259,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)],[473]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_0) ).
thf(1418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1030,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Otan ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__inverse_0) ).
thf(3453,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Otan ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(560,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_1) ).
thf(2451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(1066,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__eq__cancel2_0) ).
thf(3527,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(1041,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__unique_0) ).
thf(3473,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1022,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(3438,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(294,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(1864,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)],[294]) ).
thf(776,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(2925,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)],[776]) ).
thf(346,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(1978,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(486,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(2291,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)],[486]) ).
thf(471,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(2254,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)],[471]) ).
thf(1085,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_0) ).
thf(3569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(603,axiom,
! [A: $i] :
~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__not__less__self_0) ).
thf(2540,plain,
! [A: $i] :
~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(373,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(2034,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)],[373]) ).
thf(339,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(1960,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)],[339]) ).
thf(609,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(2555,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)],[609]) ).
thf(957,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Transcendental_Ocos @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__less__zero_0) ).
thf(3300,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Transcendental_Ocos @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(858,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__45_0) ).
thf(3093,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1581,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(506,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(2335,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)],[506]) ).
thf(709,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
thf(2777,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(883,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_0) ).
thf(3152,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1157,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(3712,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)],[1157]) ).
thf(707,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__pos_0) ).
thf(2772,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(62,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(1351,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)],[62]) ).
thf(698,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_3) ).
thf(2750,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(722,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(2804,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)],[722]) ).
thf(176,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(1600,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)],[176]) ).
thf(683,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(2718,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(345,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(1975,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)],[345]) ).
thf(995,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(3378,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_6) ).
thf(1843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(385,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(2058,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)],[385]) ).
thf(519,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(2367,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)],[519]) ).
thf(553,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(2437,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)],[553]) ).
thf(844,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
thf(3068,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(73,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(1377,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)],[73]) ).
thf(1171,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(3739,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(482,axiom,
! [A: $i] :
( ( ( A @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_Transcendental_Ocos )
!= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__one__sin__zero_0) ).
thf(2281,plain,
! [A: $i] :
( ( ( A @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_Transcendental_Ocos )
!= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(309,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(1896,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)],[309]) ).
thf(1014,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_0) ).
thf(3421,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(105,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__sgn_0) ).
thf(1447,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(575,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(2483,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)],[575]) ).
thf(1056,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
thf(3505,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1142,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ ( A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ ( A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__MVT_0) ).
thf(3685,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ ( A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ ( A @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1206,axiom,
! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).
thf(3808,plain,
! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_H_0) ).
thf(1796,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(546,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(2424,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)],[546]) ).
thf(144,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(1526,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)],[144]) ).
thf(1138,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power2_0) ).
thf(3676,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(720,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(2799,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)],[720]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_2) ).
thf(2639,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(970,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_1) ).
thf(3327,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(98,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(1433,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)],[98]) ).
thf(919,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_realpow__two__sum__zero__iff_1) ).
thf(3226,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(331,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(1943,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1095,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(3588,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)],[1095]) ).
thf(12,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__gt__zero_0) ).
thf(1242,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1080,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).
thf(3559,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1103,axiom,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).
thf(3606,plain,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(140,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_Int_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).
thf(1521,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_Int_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(897,axiom,
tc_RealDef_Oreal @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
thf(3184,plain,
tc_RealDef_Oreal @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(623,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(2586,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)],[623]) ).
thf(803,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(2982,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)],[803]) ).
thf(293,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
thf(1863,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(790,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(2954,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)],[790]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_8) ).
thf(1604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(937,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(3265,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(410,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(2118,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)],[410]) ).
thf(115,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(1470,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)],[115]) ).
thf(296,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(1868,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)],[296]) ).
thf(1198,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__less__4_0) ).
thf(3795,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_0) ).
thf(2011,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(860,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__number__of_0) ).
thf(3097,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1092,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oabs__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
thf(3582,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oabs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(920,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).
thf(3229,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1029,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_3) ).
thf(3450,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(1055,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__squared__add_0) ).
thf(3503,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1034,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).
thf(3459,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1096,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__zero_0) ).
thf(3591,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(770,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(2910,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)],[770]) ).
thf(958,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(3301,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)],[958]) ).
thf(446,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(2204,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)],[446]) ).
thf(618,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(2574,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)],[618]) ).
thf(100,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(1438,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1161,axiom,
! [B: $i,A: $i] :
~ ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I14_J_0) ).
thf(3720,plain,
! [B: $i,A: $i] :
~ ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(1117,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(3635,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)],[1117]) ).
thf(518,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(2364,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)],[518]) ).
thf(428,axiom,
! [A: $i] : ( tc_Int_Oint @ ( A @ ( A @ c_HOL_Oeq__class_Oeq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__refl_0) ).
thf(2164,plain,
! [A: $i] : ( tc_Int_Oint @ ( A @ ( A @ c_HOL_Oeq__class_Oeq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(259,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(1783,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)],[259]) ).
thf(692,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(2737,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)],[692]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
thf(2232,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( 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(493,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(2307,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)],[493]) ).
thf(836,axiom,
! [A: $i] :
~ ( tc_Int_Oint @ ( A @ c_Int_OBit1 @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I4_J_0) ).
thf(3054,plain,
! [A: $i] :
~ ( tc_Int_Oint @ ( A @ c_Int_OBit1 @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(395,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(2083,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_0) ).
thf(1736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(581,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_3) ).
thf(2496,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(715,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).
thf(2790,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1076,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__one_0) ).
thf(3550,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(358,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
thf(2000,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(192,axiom,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Oof__real ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__0_0) ).
thf(1636,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Oof__real ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(829,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__minus__half__eq_0) ).
thf(3037,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1139,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__ge2_0) ).
thf(3679,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(475,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(2264,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)],[475]) ).
thf(629,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(2601,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)],[629]) ).
thf(1102,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).
thf(3603,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
thf(1676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1105,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
thf(3610,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(992,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__squared__eq_0) ).
thf(3371,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(631,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(2606,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)],[631]) ).
thf(1209,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_3) ).
thf(3814,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(598,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( 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_sum__power2__gt__zero__iff_2) ).
thf(2528,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( 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)],[598]) ).
thf(555,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(2441,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)],[555]) ).
thf(660,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(2673,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)],[660]) ).
thf(624,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(2589,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)],[624]) ).
thf(1169,axiom,
! [B: $i,A: $i] :
~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oeq__class_Oeq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I15_J_0) ).
thf(3735,plain,
! [B: $i,A: $i] :
~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oeq__class_Oeq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(77,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(1387,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)],[77]) ).
thf(311,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(1900,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)],[311]) ).
thf(59,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(1343,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)],[59]) ).
thf(611,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_9) ).
thf(2560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(139,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(1519,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)],[139]) ).
thf(627,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(2596,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)],[627]) ).
thf(1,negated_conjecture,
( ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( v_a @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( v_r @ c_HOL_Oabs__class_Oabs ) @ c_NthRoot_Osqrt @ c_Complex_Orcis ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( v_a @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( v_r @ c_HOL_Oabs__class_Oabs ) @ c_NthRoot_Osqrt @ c_Complex_Orcis ) @ c_HOL_Otimes__class_Otimes ) ) )
!= ( v_a @ ( tc_RealDef_Oreal @ ( v_r @ c_HOL_Oabs__class_Oabs ) @ c_Complex_Orcis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1217,plain,
( ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( v_a @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( v_r @ c_HOL_Oabs__class_Oabs ) @ c_NthRoot_Osqrt @ c_Complex_Orcis ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( v_a @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( v_r @ c_HOL_Oabs__class_Oabs ) @ c_NthRoot_Osqrt @ c_Complex_Orcis ) @ c_HOL_Otimes__class_Otimes ) ) )
!= ( v_a @ ( tc_RealDef_Oreal @ ( v_r @ c_HOL_Oabs__class_Oabs ) @ c_Complex_Orcis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(421,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(2147,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)],[421]) ).
thf(924,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
thf(3239,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(845,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(3069,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(276,axiom,
tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).
thf(1824,plain,
tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(184,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_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__add__less_0) ).
thf(1619,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_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(761,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__add_0) ).
thf(2890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(541,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(2414,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)],[541]) ).
thf(910,axiom,
! [B: $i,A: $i] :
( ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
thf(3207,plain,
! [B: $i,A: $i] :
( ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(533,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(2396,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)],[533]) ).
thf(975,axiom,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).
thf(3339,plain,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(1190,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__numeral__1_0) ).
thf(3778,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(10,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(1238,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(365,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(2015,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)],[365]) ).
thf(949,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__sqrt__hcomplex__capprox_0) ).
thf(3286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(303,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
thf(1883,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(939,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__real__sqrt__sumsq_0) ).
thf(3269,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(572,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(2477,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)],[572]) ).
thf(1089,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(3578,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(335,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(1951,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)],[335]) ).
thf(1160,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_0) ).
thf(3718,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(632,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(2609,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)],[632]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(2179,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(880,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__double__less__one_0) ).
thf(3144,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(261,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(1787,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)],[261]) ).
thf(201,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(1656,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)],[201]) ).
thf(825,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(3028,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__sgn_1) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(191,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(1634,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)],[191]) ).
thf(316,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(1910,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)],[316]) ).
thf(163,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osgn__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osgn__if) ).
thf(1573,plain,
tc_Int_Oint @ class_Ring__and__Field_Osgn__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1026,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(3445,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)],[1026]) ).
thf(946,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
thf(3282,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(792,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_8) ).
thf(2958,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(960,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
thf(3307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(889,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__60_0) ).
thf(3166,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(557,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(2445,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)],[557]) ).
thf(901,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(3191,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(329,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(1938,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)],[329]) ).
thf(342,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(1968,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)],[342]) ).
thf(856,axiom,
tc_RealDef_Oreal @ class_Int_Onumber,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber) ).
thf(3090,plain,
tc_RealDef_Oreal @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(155,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(1555,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)],[155]) ).
thf(504,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_6) ).
thf(2332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(731,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(2826,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)],[731]) ).
thf(965,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 @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
thf(3314,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 @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(728,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_4) ).
thf(2820,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(876,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(3137,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)],[876]) ).
thf(1053,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
thf(3499,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(842,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(3065,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(1178,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
thf(3750,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(1100,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(3600,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(109,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(1457,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)],[109]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(187,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(1624,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)],[187]) ).
thf(501,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(2327,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)],[501]) ).
thf(450,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
thf(2213,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(579,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(2492,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)],[579]) ).
thf(606,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Otan @ ( A @ c_Transcendental_Otan @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Otan @ ( A @ c_Transcendental_Otan @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__add_0) ).
thf(2547,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Otan @ ( A @ c_Transcendental_Otan @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Otan @ ( A @ c_Transcendental_Otan @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(509,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(2344,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)],[509]) ).
thf(328,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(1936,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)],[328]) ).
thf(1037,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(3467,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(582,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
thf(2498,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(349,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_5) ).
thf(1983,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(721,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_RealVector_Oof__real ) )
!= ( A @ ( C @ c_RealVector_Oof__real ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
thf(2801,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_RealVector_Oof__real ) )
!= ( A @ ( C @ c_RealVector_Oof__real ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(268,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(1804,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)],[268]) ).
thf(739,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(2841,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)],[739]) ).
thf(997,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__algebra__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
thf(3381,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_1) ).
thf(1425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(747,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ 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__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
thf(2858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ 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__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(850,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_4) ).
thf(3078,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
thf(3650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(923,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(3237,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)],[923]) ).
thf(909,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__add__half__cancel_1) ).
thf(3205,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(738,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(2840,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(409,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(2115,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)],[409]) ).
thf(1045,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(3482,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)],[1045]) ).
thf(932,axiom,
tc_RealDef_Oreal @ class_Int_Oring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).
thf(3254,plain,
tc_RealDef_Oreal @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(402,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(2100,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)],[402]) ).
thf(1011,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__eq__square__number__of_0) ).
thf(3413,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Odiff_0) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_3) ).
thf(1772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(871,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(3122,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)],[871]) ).
thf(786,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(2946,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)],[786]) ).
thf(147,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(1534,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)],[147]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oeq__class_Oeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I13_J_0) ).
thf(1794,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oeq__class_Oeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_3) ).
thf(1953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(667,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
thf(2685,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(516,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(2359,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)],[516]) ).
thf(798,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
thf(2973,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(679,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_Transcendental_Osin @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__le__one_0) ).
thf(2709,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_Transcendental_Osin @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(343,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(1970,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)],[343]) ).
thf(5,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(1227,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)],[5]) ).
thf(914,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_realpow__two__sum__zero__iff_0) ).
thf(3218,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(290,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(1856,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)],[290]) ).
thf(670,axiom,
tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
thf(2692,plain,
tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(128,axiom,
tc_RealDef_Oreal @ ( c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__is__zero_0) ).
thf(1498,plain,
tc_RealDef_Oreal @ ( c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(170,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(1587,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)],[170]) ).
thf(589,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(2509,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)],[589]) ).
thf(1152,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(3704,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(149,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
thf(1540,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1061,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(3518,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(687,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(2726,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)],[687]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(2631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1115,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
thf(3632,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(870,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__eq__power2_0) ).
thf(3119,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1176,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__number__of__Bit1_0) ).
thf(3746,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(839,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__of__halves_0) ).
thf(3060,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(894,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__30_0) ).
thf(3176,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(854,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
thf(3087,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(82,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(1397,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)],[82]) ).
thf(53,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(1329,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)],[53]) ).
thf(755,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(2877,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)],[755]) ).
thf(66,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(1361,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)],[66]) ).
thf(810,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).
thf(3000,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(733,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(2830,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1165,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_two__realpow__ge__one_0) ).
thf(3728,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1098,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I3_J_1) ).
thf(3596,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(1163,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(3723,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)],[1163]) ).
thf(711,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
thf(2781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(564,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(2460,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(719,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(2798,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(213,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(1683,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)],[213]) ).
thf(37,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(1292,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)],[37]) ).
thf(1109,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(3622,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)],[1109]) ).
thf(1008,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(3407,plain,
! [A: $i] :
~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(911,axiom,
! [A: $i] :
( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__number__of__Pls_0) ).
thf(3210,plain,
! [A: $i] :
( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(1024,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_1) ).
thf(3441,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(815,axiom,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Complex_Orcis ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__mod__rcis_0) ).
thf(3010,plain,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Complex_Orcis ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
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(1414,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(443,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(2196,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)],[443]) ).
thf(634,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(2613,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)],[634]) ).
thf(827,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__divide_0) ).
thf(3032,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(903,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(3194,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(511,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_2) ).
thf(2349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(306,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(1889,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)],[306]) ).
thf(1078,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__of__real_0) ).
thf(3555,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(195,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(1644,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)],[195]) ).
thf(181,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(1612,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(649,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(2649,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)],[649]) ).
thf(801,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(2978,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)],[801]) ).
thf(570,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__one_0) ).
thf(2472,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(497,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(2317,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)],[497]) ).
thf(954,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
thf(3294,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(240,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(1744,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)],[240]) ).
thf(926,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
thf(3242,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( B @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( B @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__diff2_0) ).
thf(1263,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( B @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( B @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(491,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_5) ).
thf(2304,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(75,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(1382,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)],[75]) ).
thf(577,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(2487,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)],[577]) ).
thf(1174,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
thf(3743,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(514,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(2355,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)],[514]) ).
thf(621,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(2581,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)],[621]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_0) ).
thf(2006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(614,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(2566,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)],[614]) ).
thf(333,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(1947,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)],[333]) ).
thf(80,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(1393,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)],[80]) ).
thf(1151,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__mult__ge__zero_0) ).
thf(3703,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(277,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(1825,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)],[277]) ).
thf(796,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(2968,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)],[796]) ).
thf(779,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_5) ).
thf(2932,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1047,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half__gt__zero_0) ).
thf(3486,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_6) ).
thf(1478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(594,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(2519,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)],[594]) ).
thf(601,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(2536,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)],[601]) ).
thf(1072,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__numeral__1_0) ).
thf(3541,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(529,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(2387,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)],[529]) ).
thf(280,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sgn__def_0) ).
thf(1831,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(7,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(1231,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)],[7]) ).
thf(424,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(2153,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)],[424]) ).
thf(765,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
thf(2900,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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__number__of_0) ).
thf(1552,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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)],[154]) ).
thf(743,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(2851,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)],[743]) ).
thf(465,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
thf(2243,plain,
tc_Int_Oint @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(586,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
thf(2505,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1212,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__add__half__cancel_0) ).
thf(3819,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(1112,axiom,
! [A: $i] :
( ( A @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Osin @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__def_0) ).
thf(3628,plain,
! [A: $i] :
( ( A @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Osin @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(299,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_Transcendental_Ocos @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__le__one_0) ).
thf(1874,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_Transcendental_Ocos @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(868,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__30_0) ).
thf(3115,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(96,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(1429,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)],[96]) ).
thf(928,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_realpow__two__sum__zero__iff_2) ).
thf(3247,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(1009,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_4) ).
thf(3409,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(749,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
thf(2862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(382,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(2052,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)],[382]) ).
thf(15,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(1246,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)],[15]) ).
thf(347,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(1979,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)],[347]) ).
thf(812,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( D @ ( C @ c_Complex_Orcis ) @ ( B @ ( A @ c_Complex_Orcis ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Complex_Orcis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rcis__mult_0) ).
thf(3005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( D @ ( C @ c_Complex_Orcis ) @ ( B @ ( A @ c_Complex_Orcis ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Complex_Orcis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(478,axiom,
tc_Int_Oint @ class_Int_Oring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(2272,plain,
tc_Int_Oint @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(988,axiom,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
thf(3364,plain,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(520,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(2370,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)],[520]) ).
thf(913,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
thf(3215,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(143,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
thf(1525,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1180,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 @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
thf(3755,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 @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1215,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(3824,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1204,axiom,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__1__eq__1_0) ).
thf(3802,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(918,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
thf(3225,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(676,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(2702,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)],[676]) ).
thf(448,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(2208,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)],[448]) ).
thf(218,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(1695,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)],[218]) ).
thf(757,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_7) ).
thf(2883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_6) ).
thf(1563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(697,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_9) ).
thf(2748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(772,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(2915,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)],[772]) ).
thf(1057,axiom,
! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
| ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__1__iff_0) ).
thf(3508,plain,
! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
| ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(647,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__diff__triangle__ineq_0) ).
thf(2645,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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__number__of_3) ).
thf(2617,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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)],[636]) ).
thf(1042,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
thf(3476,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(55,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(1333,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)],[55]) ).
thf(353,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(1991,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)],[353]) ).
thf(714,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(2788,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)],[714]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_9) ).
thf(1318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(794,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(2963,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)],[794]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(538,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(2408,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)],[538]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_1) ).
thf(2089,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(900,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(3190,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(137,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(1515,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)],[137]) ).
thf(454,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(2221,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)],[454]) ).
thf(507,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(2338,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)],[507]) ).
thf(356,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(1996,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)],[356]) ).
thf(1137,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(3675,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(314,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(1906,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)],[314]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(2001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(17,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1251,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(245,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_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__triangle__ineq4_0) ).
thf(1754,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_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(219,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1698,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1049,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_3) ).
thf(3491,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__class_Oeq__refl_0) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(241,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1747,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(323,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(1927,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)],[323]) ).
thf(936,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(3262,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)],[936]) ).
thf(951,axiom,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Pls_0) ).
thf(3289,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(1197,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_2) ).
thf(3792,plain,
! [A: $i] :
( ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(866,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Olordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
thf(3111,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Olordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(596,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(2524,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)],[596]) ).
thf(190,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
thf(1631,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(886,axiom,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I50_J_0) ).
thf(3158,plain,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(411,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(2121,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)],[411]) ).
thf(461,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(2235,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)],[461]) ).
thf(420,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(2144,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)],[420]) ).
thf(781,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(2936,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)],[781]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_0) ).
thf(1648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1154,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__ge__zero_0) ).
thf(3707,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(232,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(1727,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)],[232]) ).
thf(662,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(2677,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(435,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(2176,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)],[435]) ).
thf(531,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(2391,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)],[531]) ).
thf(767,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(2904,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)],[767]) ).
thf(984,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__gt__zero_0) ).
thf(3358,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(422,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(2149,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)],[422]) ).
thf(370,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
thf(2028,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(174,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(1595,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)],[174]) ).
thf(763,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
thf(2894,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(72,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(1374,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)],[72]) ).
thf(1069,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half_0) ).
thf(3536,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(846,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__gt__half__sum_0) ).
thf(3070,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(797,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
thf(2970,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1185,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_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
thf(3768,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_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1062,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
thf(3519,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(2188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(578,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(2489,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)],[578]) ).
thf(807,axiom,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ c_HOL_Oabs__class_Oabs ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
| ( ( A @ c_Transcendental_Osin )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero__abs__cos__one_0) ).
thf(2991,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ c_HOL_Oabs__class_Oabs ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
| ( ( A @ c_Transcendental_Osin )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_3) ).
thf(2716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(341,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(1965,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)],[341]) ).
thf(727,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
thf(2817,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(416,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(2134,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)],[416]) ).
thf(1173,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_5) ).
thf(3741,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1075,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__power2_0) ).
thf(3547,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(281,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(1833,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)],[281]) ).
thf(379,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(2048,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)],[379]) ).
thf(782,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_4) ).
thf(2938,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(456,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(2225,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)],[456]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1884,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(182,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(1615,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)],[182]) ).
thf(78,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(1389,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(933,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_4) ).
thf(3255,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__less_0) ).
thf(3811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(925,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__double_0) ).
thf(3240,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1104,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(3609,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(742,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(2849,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)],[742]) ).
thf(532,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).
thf(2393,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(244,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(1752,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)],[244]) ).
thf(199,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(1652,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)],[199]) ).
thf(851,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 ) ) )
| ( B = C )
| ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__eq__imp__eq_0) ).
thf(3081,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 ) ) )
| ( B = C )
| ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(1181,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(3758,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_7) ).
thf(1929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(947,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_1) ).
thf(3283,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(938,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__divide_0) ).
thf(3266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(591,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(2514,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)],[591]) ).
thf(615,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(2568,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( 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_sum__power2__gt__zero__iff_1) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( 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)],[85]) ).
thf(1033,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(3458,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).
thf(1701,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(534,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(2398,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)],[534]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_1) ).
thf(1488,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(672,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(2695,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_2) ).
thf(1256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(916,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(3223,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1187,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(3773,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_5) ).
thf(2029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(2293,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1164,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__squared__add2_0) ).
thf(3726,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(46,axiom,
( c_Transcendental_Opi
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
thf(1312,plain,
( c_Transcendental_Opi
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1148,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
thf(3695,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1130,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_1) ).
thf(3663,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(11,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(1239,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)],[11]) ).
thf(1021,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_2) ).
thf(3436,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1192,axiom,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
thf(3783,plain,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(678,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(2706,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)],[678]) ).
thf(1012,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__mult_0) ).
thf(3416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(21,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(1258,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)],[21]) ).
thf(959,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_3) ).
thf(3304,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__square__gt__zero2_0) ).
thf(1356,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1199,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
thf(3796,plain,
tc_Complex_Ocomplex @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(131,axiom,
tc_nat @ class_HOL_Oeq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oeq) ).
thf(1503,plain,
tc_nat @ class_HOL_Oeq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(822,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
thf(3023,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(207,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(1669,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)],[207]) ).
thf(441,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(2193,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(260,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
thf(1786,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(811,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(3002,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)],[811]) ).
thf(235,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(1733,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)],[235]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1108,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(3619,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)],[1108]) ).
thf(1090,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Transcendental_Ocos @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__le__zero_0) ).
thf(3579,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Transcendental_Ocos @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(610,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_1) ).
thf(2557,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1119,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_realpow__two__le__add__order_0) ).
thf(3641,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(857,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_0) ).
thf(3091,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(112,axiom,
! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sgn__def_1) ).
thf(1464,plain,
! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(983,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( 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__power2_1) ).
thf(3355,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( 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)],[983]) ).
thf(4,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_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(1224,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_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(595,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(2521,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)],[595]) ).
thf(982,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(3352,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)],[982]) ).
thf(930,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(3251,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(545,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(2422,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)],[545]) ).
thf(658,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(2669,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)],[658]) ).
thf(1156,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos @ c_HOL_Ominus__class_Ominus ) ) @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Osin @ c_HOL_Ominus__class_Ominus ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__add_0) ).
thf(3710,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos @ c_HOL_Ominus__class_Ominus ) ) @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Osin @ c_HOL_Ominus__class_Ominus ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(267,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(1801,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)],[267]) ).
thf(746,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(2856,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)],[746]) ).
thf(43,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(1307,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)],[43]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(2361,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(495,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(2311,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)],[495]) ).
thf(1114,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(3631,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(602,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(2538,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)],[602]) ).
thf(289,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(1853,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)],[289]) ).
thf(423,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(2151,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)],[423]) ).
thf(646,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(2642,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)],[646]) ).
thf(884,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(3155,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(458,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(2229,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(396,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( B @ c_HOL_Osgn__class_Osgn ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
thf(2084,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( B @ c_HOL_Osgn__class_Osgn ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(451,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(2214,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)],[451]) ).
thf(525,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(2383,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1183,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(3764,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_0) ).
thf(1894,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(805,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(2987,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)],[805]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_6) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(269,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(1806,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)],[269]) ).
thf(1141,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oeq__class_Oeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I9_J_0) ).
thf(3683,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oeq__class_Oeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(142,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1524,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(768,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(2906,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)],[768]) ).
thf(1013,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__mult__squared__eq_0) ).
thf(3419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(61,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(1349,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)],[61]) ).
thf(401,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(2097,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)],[401]) ).
thf(940,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(3270,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)],[940]) ).
thf(1167,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(3732,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(483,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
thf(2284,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( 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(326,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(1933,plain,
tc_nat @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(2257,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_4) ).
thf(1589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(467,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(2246,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)],[467]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_3) ).
thf(1492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(177,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(1603,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(863,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(3106,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(1038,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
thf(3468,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(523,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(2378,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)],[523]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__le__imp__le_0) ).
thf(3066,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(1094,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
thf(3586,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_4) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(753,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ratiotest__lemma_0) ).
thf(2871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(101,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(1439,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)],[101]) ).
thf(437,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(2182,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)],[437]) ).
thf(301,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(1877,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)],[301]) ).
thf(57,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(1339,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)],[57]) ).
thf(874,axiom,
( ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__pi_0) ).
thf(3133,plain,
( ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(407,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(2111,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)],[407]) ).
thf(354,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(1993,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)],[354]) ).
thf(476,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(2267,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)],[476]) ).
thf(1086,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(3572,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)],[1086]) ).
thf(701,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(2757,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)],[701]) ).
thf(902,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__average__minus__second_0) ).
thf(3192,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(713,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
thf(2785,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1093,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__of__real__divide_0) ).
thf(3583,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(481,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(2278,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)],[481]) ).
thf(777,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(2928,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)],[777]) ).
thf(502,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
thf(2329,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(680,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(2710,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)],[680]) ).
thf(1032,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__45_0) ).
thf(3456,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(206,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(1667,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)],[206]) ).
thf(369,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(2025,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)],[369]) ).
thf(725,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__squared__add3_0) ).
thf(2812,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
thf(2314,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(639,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(2625,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)],[639]) ).
thf(275,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(1821,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)],[275]) ).
thf(234,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(1731,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)],[234]) ).
thf(1202,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(3800,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(828,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(3034,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)],[828]) ).
thf(539,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(2410,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)],[539]) ).
thf(775,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ 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_not__sum__power2__lt__zero_0) ).
thf(2923,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ 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)],[775]) ).
thf(283,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(1838,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)],[283]) ).
thf(51,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(1325,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)],[51]) ).
thf(956,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Osin )
= ( A @ c_Transcendental_Osin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__periodic_0) ).
thf(3298,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Osin )
= ( A @ c_Transcendental_Osin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(754,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(2874,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)],[754]) ).
thf(604,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(2542,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)],[604]) ).
thf(485,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
thf(2289,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(648,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_6) ).
thf(2647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_7) ).
thf(2252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(655,axiom,
tc_Int_Oint @ ( c_Int_OPls @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I1_J_0) ).
thf(2664,plain,
tc_Int_Oint @ ( c_Int_OPls @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(565,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(2461,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)],[565]) ).
thf(799,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(2974,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)],[799]) ).
thf(620,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(2578,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)],[620]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_1) ).
thf(1688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1044,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).
thf(3480,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(432,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(2171,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)],[432]) ).
thf(736,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(2835,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)],[736]) ).
thf(865,axiom,
tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__ge__two_0) ).
thf(3110,plain,
tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(879,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__real__divide__sqrt__less_0) ).
thf(3142,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_8) ).
thf(1496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(895,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2_0) ).
thf(3178,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(671,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(2693,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)],[671]) ).
thf(587,axiom,
tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
thf(2506,plain,
tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1071,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I9_J_1) ).
thf(3539,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(392,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(2075,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)],[392]) ).
thf(543,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(2418,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)],[543]) ).
thf(81,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
thf(1396,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(554,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_6) ).
thf(2439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ( B = C )
| ~ ( A @ class_HOL_Oeq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equals_0) ).
thf(2401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ( B = C )
| ~ ( A @ class_HOL_Oeq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__triangle__ineq3_0) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(381,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(2051,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(704,axiom,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
thf(2765,plain,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1015,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_RealVector_Oreal__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__divide_0) ).
thf(3423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_RealVector_Oreal__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__triangle__ineq2_0) ).
thf(2550,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(14,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1245,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(574,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(2481,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)],[574]) ).
thf(104,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(1445,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)],[104]) ).
thf(637,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(2620,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)],[637]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).
thf(2139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(1143,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(3687,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(388,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(2064,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)],[388]) ).
thf(1136,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__gt__zero_0) ).
thf(3674,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(466,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I13_J_1) ).
thf(2244,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oeq__class_Oeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(699,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
thf(2752,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(643,axiom,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Oof__real ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Ozero_0) ).
thf(2633,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Oof__real ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(2022,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(987,axiom,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(3363,plain,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(962,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__add_0) ).
thf(3310,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(979,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sq__order_0) ).
thf(3348,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(2156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(390,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(2069,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)],[390]) ).
thf(751,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_4) ).
thf(2867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(188,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(1626,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)],[188]) ).
thf(383,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(2054,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)],[383]) ).
thf(168,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(1583,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)],[168]) ).
thf(204,axiom,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_RealVector_Oof__real ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__1_0) ).
thf(1662,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_RealVector_Oof__real ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(656,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(2665,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)],[656]) ).
thf(1003,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(3395,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)],[1003]) ).
thf(953,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(3293,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(2037,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(585,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(2503,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(29,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(1277,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)],[29]) ).
thf(881,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(3146,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)],[881]) ).
thf(641,axiom,
( ( c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__is__zero_2) ).
thf(2629,plain,
( ( c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(666,axiom,
tc_Int_Oint @ class_HOL_Oeq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__HOL_Oeq) ).
thf(2684,plain,
tc_Int_Oint @ class_HOL_Oeq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(1031,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__gt__one_0) ).
thf(3455,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(338,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(1958,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)],[338]) ).
thf(952,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(3292,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(1025,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__ge__zero_0) ).
thf(3444,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_7) ).
thf(2239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(247,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_5) ).
thf(1758,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_1) ).
thf(2107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(113,axiom,
( ( c_Transcendental_Opi @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__pi_0) ).
thf(1467,plain,
( ( c_Transcendental_Opi @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(808,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_4) ).
thf(2994,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(887,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__pow2_0) ).
thf(3161,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1135,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
thf(3672,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(92,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(1420,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)],[92]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(2449,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(134,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(1509,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)],[134]) ).
thf(741,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(2846,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)],[741]) ).
thf(613,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(2564,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)],[613]) ).
thf(784,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(2942,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)],[784]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_8) ).
thf(1845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(175,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(1598,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)],[175]) ).
thf(867,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(3112,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)],[867]) ).
thf(654,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(2661,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)],[654]) ).
thf(522,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(2375,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)],[522]) ).
thf(935,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ c_HOL_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sgn__eq_0) ).
thf(3260,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ c_HOL_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1128,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_4) ).
thf(3659,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(663,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(2678,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(257,axiom,
tc_nat @ class_Int_Onumber,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(1780,plain,
tc_nat @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(685,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
thf(2720,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(152,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_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__triangle__ineq_0) ).
thf(1547,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_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_8) ).
thf(1748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(266,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(1798,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)],[266]) ).
thf(489,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(2298,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)],[489]) ).
thf(1001,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(3391,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)],[1001]) ).
thf(1170,axiom,
! [A: $i] :
( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Osin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__sin__eq_0) ).
thf(3737,plain,
! [A: $i] :
( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Osin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(994,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(3376,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)],[994]) ).
thf(386,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_2) ).
thf(2060,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(239,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
thf(1743,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(690,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(2732,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)],[690]) ).
thf(18,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(1252,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)],[18]) ).
thf(1035,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(3462,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(528,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
thf(2386,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1193,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__average__minus__first_0) ).
thf(3786,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(25,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(1267,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)],[25]) ).
thf(616,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(2569,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)],[616]) ).
thf(1120,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel_0) ).
thf(3642,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(399,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
thf(2092,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(841,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squared__expand_0) ).
thf(3063,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1162,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__triangle__ineq_0) ).
thf(3722,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(977,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
thf(3344,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1073,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(3544,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1082,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(3564,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(166,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(1579,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)],[166]) ).
thf(1158,axiom,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).
thf(3715,plain,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(652,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_1) ).
thf(2656,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__pos_0) ).
thf(1711,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(129,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(1499,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)],[129]) ).
thf(351,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(1987,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)],[351]) ).
thf(227,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(1716,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(561,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_8) ).
thf(2454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(429,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(2165,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)],[429]) ).
thf(1211,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(3818,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1813,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_7) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1146,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__eq__power2_1) ).
thf(3691,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__diff__ineq_0) ).
thf(2688,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(941,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( B @ ( A @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__power_0) ).
thf(3273,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( B @ ( A @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(973,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).
thf(3334,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1196,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(3791,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(824,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_3) ).
thf(3026,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(548,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_2) ).
thf(2429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(1126,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_0) ).
thf(3655,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(9,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(1235,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)],[9]) ).
thf(480,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(2276,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)],[480]) ).
thf(1203,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(3801,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(414,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(2128,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)],[414]) ).
thf(1188,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 ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
thf(3774,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 ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_2) ).
thf(1763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).
thf(1658,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(499,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(2322,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)],[499]) ).
thf(675,axiom,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
thf(2701,plain,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(628,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(2599,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)],[628]) ).
thf(971,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).
thf(3329,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(892,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(3174,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_0) ).
thf(1738,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(832,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rabs__ratiotest__lemma_0) ).
thf(3041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(859,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( 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__power2_0) ).
thf(3095,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( 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)],[859]) ).
thf(568,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_5) ).
thf(2468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(2,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(1220,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)],[2]) ).
thf(310,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(1898,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)],[310]) ).
thf(408,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(2113,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)],[408]) ).
thf(348,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(1981,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)],[348]) ).
thf(32,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(1284,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)],[32]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(1585,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(823,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half__gt__zero__iff_0) ).
thf(3024,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(71,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(1372,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)],[71]) ).
thf(1063,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__abs2_0) ).
thf(3520,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(813,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(3007,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1004,axiom,
( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__one_0) ).
thf(3398,plain,
( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(950,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(3288,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_7) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(661,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(2675,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)],[661]) ).
thf(384,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_4) ).
thf(2056,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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(327,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(1934,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)],[327]) ).
thf(787,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(2948,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)],[787]) ).
thf(1149,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(3697,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1048,axiom,
! [A: $i] :
( ( c_Int_OPls = A )
| ( c_Int_OPls
!= ( A @ c_Int_OBit0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).
thf(3488,plain,
! [A: $i] :
( ( c_Int_OPls = A )
| ( c_Int_OPls
!= ( A @ c_Int_OBit0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(583,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_4) ).
thf(2500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__add_0) ).
thf(1543,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(864,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__neq__two_0) ).
thf(3107,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(515,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(2357,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)],[515]) ).
thf(337,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(1955,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)],[337]) ).
thf(121,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1485,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(344,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(1972,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)],[344]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__ge__zero_0) ).
thf(2320,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(917,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
thf(3224,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(95,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(1427,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)],[95]) ).
thf(1000,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__neq__zero_0) ).
thf(3388,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(132,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(1504,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)],[132]) ).
thf(869,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__one__imp__sqr__less__one_0) ).
thf(3117,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(748,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(2860,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)],[748]) ).
thf(688,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(2728,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(228,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(1717,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(723,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(2807,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)],[723]) ).
thf(885,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__pi__half_0) ).
thf(3156,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1019,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(3433,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(877,axiom,
tc_RealDef_Oreal @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
thf(3139,plain,
tc_RealDef_Oreal @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(573,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(2479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1083,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(3565,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(673,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(2696,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)],[673]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
thf(2078,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(500,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__ge__zero_0) ).
thf(2325,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_5) ).
thf(1781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1110,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
thf(3625,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(716,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__diff_0) ).
thf(2792,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Osin @ ( A @ c_Transcendental_Osin @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(890,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
thf(3168,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(330,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(1940,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)],[330]) ).
thf(552,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(2435,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)],[552]) ).
thf(702,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(2760,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)],[702]) ).
thf(364,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(2013,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)],[364]) ).
thf(1005,axiom,
! [A: $i] :
( ( A @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Ocos ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__eq_0) ).
thf(3400,plain,
! [A: $i] :
( ( A @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Ocos ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_1) ).
thf(2045,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(214,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(1685,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)],[214]) ).
thf(758,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
thf(2885,plain,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(1949,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(732,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(2828,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)],[732]) ).
thf(891,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
thf(3171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(793,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(2960,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)],[793]) ).
thf(1068,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).
thf(3533,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(1027,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__abs_0) ).
thf(3447,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(899,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__zero_0) ).
thf(3188,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(442,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(2194,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)],[442]) ).
thf(510,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(2347,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)],[510]) ).
thf(200,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(1654,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)],[200]) ).
thf(694,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
thf(2743,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(809,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power3__eq__cube_0) ).
thf(2997,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(967,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__45_0) ).
thf(3320,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(35,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(1289,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(837,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osgn__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).
thf(3056,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osgn__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
thf(1866,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(708,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(2775,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)],[708]) ).
thf(1131,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(3665,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(830,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(3039,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(357,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(1998,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)],[357]) ).
thf(1200,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(3797,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1097,axiom,
! [A: $i] :
( ( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Otan @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__double_0) ).
thf(3593,plain,
! [A: $i] :
( ( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Otan @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1166,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
thf(3729,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1106,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(3613,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)],[1106]) ).
thf(58,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(1341,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)],[58]) ).
thf(537,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_8) ).
thf(2406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1054,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__divide__square__eq_0) ).
thf(3501,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(931,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
= ( A @ c_Transcendental_Otan ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic_0) ).
thf(3252,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
= ( A @ c_Transcendental_Otan ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(853,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Orcis ) )
= ( tc_Complex_Ocomplex @ ( B @ c_Complex_Ocis @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rcis__def_0) ).
thf(3085,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Orcis ) )
= ( tc_Complex_Ocomplex @ ( B @ c_Complex_Ocis @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1036,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I3_J_0) ).
thf(3465,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oeq__class_Oeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(625,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(2591,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)],[625]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_0) ).
thf(1646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ 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__abs_0) ).
thf(2443,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ 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)],[556]) ).
thf(626,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(2594,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)],[626]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Otan @ ( A @ c_Transcendental_Otan @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Osin @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__tan__eq_0) ).
thf(1721,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Otan @ ( A @ c_Transcendental_Otan @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Osin @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(430,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(2167,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)],[430]) ).
thf(479,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(2273,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)],[479]) ).
thf(434,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(2174,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)],[434]) ).
thf(530,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_1) ).
thf(2389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(117,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(1476,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)],[117]) ).
thf(209,axiom,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__zero_0) ).
thf(1674,plain,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Transcendental_Otan )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(745,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
thf(2855,plain,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(193,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(1639,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)],[193]) ).
thf(744,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(2853,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)],[744]) ).
thf(1216,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I110_J_0) ).
thf(3825,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(991,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__60_0) ).
thf(3369,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(730,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn0_0) ).
thf(2823,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(1177,axiom,
! [A: $i] :
~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit1 @ c_HOL_Oeq__class_Oeq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__int__code_I10_J_0) ).
thf(3748,plain,
! [A: $i] :
~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit1 @ c_HOL_Oeq__class_Oeq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1113,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(3630,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1081,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(3561,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(922,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( 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_power2__less__imp__less_0) ).
thf(3235,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( 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)],[922]) ).
thf(549,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(2431,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1060,axiom,
~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
thf(3516,plain,
~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(141,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
thf(1523,plain,
tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(972,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
thf(3331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(990,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(3368,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1129,axiom,
tc_Complex_Ocomplex @ class_HOL_Oeq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Oeq) ).
thf(3662,plain,
tc_Complex_Ocomplex @ class_HOL_Oeq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(597,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(2526,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)],[597]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).
thf(2416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(156,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).
thf(1558,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(780,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( 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_sum__power2__gt__zero__iff_0) ).
thf(2934,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( 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)],[780]) ).
thf(474,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(2262,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)],[474]) ).
thf(785,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_7) ).
thf(2944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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__number__of_1) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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)],[292]) ).
thf(124,axiom,
tc_Int_Oint @ class_Int_Onumber,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
thf(1491,plain,
tc_Int_Oint @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(394,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(2081,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)],[394]) ).
thf(969,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
thf(3324,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(718,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(2796,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)],[718]) ).
thf(1052,axiom,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ c_Complex_Ocis @ ( A @ c_Complex_Ocis @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Complex_Ocis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cis__mult_0) ).
thf(3497,plain,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ c_Complex_Ocis @ ( A @ c_Complex_Ocis @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Complex_Ocis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1099,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).
thf(3598,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(619,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__squared__diff__one__factored_0) ).
thf(2576,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(223,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(1706,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)],[223]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
thf(2162,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(2680,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(981,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(3351,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(766,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(2902,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)],[766]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_1) ).
thf(2095,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(580,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_3) ).
thf(2494,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(1182,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 ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
thf(3761,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 ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1077,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_RealVector_Oof__real ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__number__of__eq_0) ).
thf(3552,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_RealVector_Oof__real ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(896,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__pow2__iff_0) ).
thf(3181,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ c_Power_Opower__class_Opower ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(526,axiom,
tc_Int_Oint @ class_Int_Onumber__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(2384,plain,
tc_Int_Oint @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(571,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(2475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1147,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(3694,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1018,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(3430,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)],[1018]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Oadd_0) ).
thf(1777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(882,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__sum__squares__eq__cancel_0) ).
thf(3149,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(503,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(2330,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)],[503]) ).
thf(459,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(2230,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)],[459]) ).
thf(374,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(2036,plain,
tc_nat @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(44,axiom,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__self__sum__ge__zero_0) ).
thf(1309,plain,
! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_0) ).
thf(3645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(484,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(2287,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)],[484]) ).
thf(403,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(2102,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)],[403]) ).
thf(593,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(2517,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)],[593]) ).
thf(1153,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(3705,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)],[1153]) ).
thf(921,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).
thf(3232,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(684,axiom,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).
thf(2719,plain,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1168,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_1) ).
thf(3733,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(861,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
thf(3100,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1064,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(3521,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)],[1064]) ).
thf(362,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(2008,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)],[362]) ).
thf(1051,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(3496,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(315,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(1908,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)],[315]) ).
thf(360,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sgn__pos_0) ).
thf(2003,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(996,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__half__sum_0) ).
thf(3379,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( C @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__power_0) ).
thf(2218,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_RealVector_Oof__real ) )
= ( A @ ( C @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(778,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(2930,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(412,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(2123,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)],[412]) ).
thf(135,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(1512,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)],[135]) ).
thf(255,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(1774,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)],[255]) ).
thf(527,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).
thf(2385,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(211,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(1678,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)],[211]) ).
thf(1058,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos )
= ( A @ c_Transcendental_Ocos ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__periodic_0) ).
thf(3511,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos )
= ( A @ c_Transcendental_Ocos ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).
thf(3601,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(993,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2__right_0) ).
thf(3373,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(173,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__gt__zero__pi_0) ).
thf(1593,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1195,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__less__two_0) ).
thf(3790,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(974,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__mult__distrib_0) ).
thf(3337,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(380,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(2050,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(705,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(2768,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)],[705]) ).
thf(1145,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(3690,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( 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_Rational_Oordered__idom__class_Osgn__greater_1) ).
thf(1480,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( 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)],[119]) ).
thf(908,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(3203,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)],[908]) ).
thf(840,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__cos__le__one_0) ).
thf(3062,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Ocos @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1039,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
thf(3469,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(888,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__gt__zero2_0) ).
thf(3164,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Osin @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(818,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
thf(3015,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_NthRoot_Osqrt @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(67,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(1363,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)],[67]) ).
thf(273,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(1816,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)],[273]) ).
thf(505,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(2334,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(944,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__abs_0) ).
thf(3277,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(1079,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(3558,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(696,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(2746,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)],[696]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).
thf(1789,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(34,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
thf(1288,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1184,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_0) ).
thf(3765,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_2) ).
thf(2040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(60,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(1346,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)],[60]) ).
thf(712,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(2783,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)],[712]) ).
thf(961,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(3309,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1214,axiom,
( ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__two__pi_0) ).
thf(3822,plain,
( ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(644,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(2636,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)],[644]) ).
thf(99,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(1436,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)],[99]) ).
thf(291,axiom,
( ( c_Transcendental_Opi @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__pi_0) ).
thf(1859,plain,
( ( c_Transcendental_Opi @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(445,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(2201,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)],[445]) ).
thf(352,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(1989,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)],[352]) ).
thf(56,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(1335,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)],[56]) ).
thf(217,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(1693,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)],[217]) ).
thf(617,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(2572,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)],[617]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_2) ).
thf(1561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(677,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(2704,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)],[677]) ).
thf(771,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(2913,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)],[771]) ).
thf(536,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(2404,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)],[536]) ).
thf(905,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(3196,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)],[905]) ).
thf(1016,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_0) ).
thf(3426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(455,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(2223,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)],[455]) ).
thf(116,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(1473,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)],[116]) ).
thf(1116,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__squared__eq_0) ).
thf(3633,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Ocos @ c_Power_Opower__class_Opower ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Transcendental_Osin @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
thf(3805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(650,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(2651,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)],[650]) ).
thf(513,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(2353,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)],[513]) ).
thf(278,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(1827,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)],[278]) ).
thf(795,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(2966,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)],[795]) ).
thf(985,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__60_0) ).
thf(3360,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ c_HOL_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(622,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(2583,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)],[622]) ).
thf(588,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(2507,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)],[588]) ).
thf(1070,axiom,
tc_RealDef_Oreal @ class_HOL_Oeq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Oeq) ).
thf(3538,plain,
tc_RealDef_Oreal @ class_HOL_Oeq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(976,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__diff_0) ).
thf(3341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(584,axiom,
tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__ge__zero_0) ).
thf(2502,plain,
tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(464,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(2241,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)],[464]) ).
thf(426,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(2159,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)],[426]) ).
thf(986,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) ).
thf(3362,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(724,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_1) ).
thf(2810,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(873,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_NthRoot_Osqrt )
!= ( B @ c_NthRoot_Osqrt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
thf(3128,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_NthRoot_Osqrt )
!= ( B @ c_NthRoot_Osqrt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_6) ).
thf(1829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(838,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel2_0) ).
thf(3057,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(146,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(1532,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)],[146]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1010,axiom,
( ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__3over2__pi_0) ).
thf(3411,plain,
( ( tc_RealDef_Oreal @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(576,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(2485,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)],[576]) ).
thf(148,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(1537,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)],[148]) ).
thf(1210,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(3817,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(927,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__abs2_0) ).
thf(3245,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(820,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
thf(3020,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(750,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(2864,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)],[750]) ).
thf(1172,axiom,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__ge__zero_0) ).
thf(3740,plain,
tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(302,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(1880,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)],[302]) ).
thf(97,axiom,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero_0) ).
thf(1431,plain,
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_Transcendental_Osin )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(849,axiom,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__two__squares__add__zero__iff_2) ).
thf(3076,plain,
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(312,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(1902,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)],[312]) ).
thf(674,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_8) ).
thf(2699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(1050,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ 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__power2_0) ).
thf(3494,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ 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)],[1050]) ).
thf(83,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(1399,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)],[83]) ).
thf(477,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(2270,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)],[477]) ).
thf(185,axiom,
tc_Int_Oint @ class_Ring__and__Field_Olordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).
thf(1621,plain,
tc_Int_Oint @ class_Ring__and__Field_Olordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of_2) ).
thf(1962,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1111,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_0) ).
thf(3626,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(912,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).
thf(3212,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(447,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_9) ).
thf(2206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( 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 @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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(734,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(2832,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)],[734]) ).
thf(90,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
thf(1416,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(397,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(2087,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)],[397]) ).
thf(1179,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_Complex_Orcis ) )
= ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Oof__real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rcis__zero__arg_0) ).
thf(3753,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_Complex_Orcis ) )
= ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Oof__real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(817,axiom,
( ( v_a @ ( v_r @ c_Complex_Orcis ) )
= ( tc_Complex_Ocomplex @ ( v_a @ c_Complex_Ocis @ ( tc_Complex_Ocomplex @ ( v_r @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rcis__def__raw_0) ).
thf(3013,plain,
( ( v_a @ ( v_r @ c_Complex_Orcis ) )
= ( tc_Complex_Ocomplex @ ( v_a @ c_Complex_Ocis @ ( tc_Complex_Ocomplex @ ( v_r @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(54,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(1331,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)],[54]) ).
thf(179,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(1606,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)],[179]) ).
thf(1091,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_0) ).
thf(3580,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(49,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(1320,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)],[49]) ).
thf(332,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(1944,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)],[332]) ).
thf(69,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(1367,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)],[69]) ).
thf(212,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(1681,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)],[212]) ).
thf(760,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(2887,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)],[760]) ).
thf(1007,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_0) ).
thf(3405,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(669,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_5) ).
thf(2690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Otan @ ( A @ c_Transcendental_Otan @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__tan__add1_0) ).
thf(1565,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ c_Transcendental_Ocos )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Otan @ ( A @ c_Transcendental_Otan @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Transcendental_Ocos @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(635,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
thf(2615,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( 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__number__of1_2) ).
thf(1769,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(319,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(1917,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)],[319]) ).
thf(735,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
thf(2834,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(512,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(2351,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)],[512]) ).
thf(907,axiom,
! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__zero__cancel_0) ).
thf(3200,plain,
! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(440,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(2191,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)],[440]) ).
thf(834,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__gt__zero_0) ).
thf(3047,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(569,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(2470,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)],[569]) ).
thf(317,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(1912,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)],[317]) ).
thf(802,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
thf(2980,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1087,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).
thf(3575,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(297,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(1870,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)],[297]) ).
thf(1133,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
thf(3669,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(706,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
thf(2771,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(3863,plain,
$false,
inference(e,[status(thm)],[2822,1501,1718,1411,2778,1995,3798,3434,2412,2463,1840,2427,3449,2544,3566,1295,1549,2250,2199,3021,1322,1665,2612,1469,2744,1369,2295,2306,3345,2341,3008,2109,2131,1454,2031,2072,1767,3666,1729,2921,3477,3698,1315,1850,3680,3317,1290,2622,3285,3040,2671,3012,1591,2837,3402,1305,3382,1486,1750,3185,2309,2512,2976,3072,1924,2210,2940,1406,3813,2381,2908,2062,1443,1808,2659,2953,1401,1422,1569,2248,3017,3530,1671,3439,3429,3648,3044,3175,2448,3781,1327,1761,3313,2844,1354,3276,3049,3745,1756,1310,3135,3649,3365,2740,2918,1275,2141,2434,1872,3616,1233,2627,1260,1919,2459,3577,2042,1507,1222,3717,3103,1835,2216,3777,1650,2173,2516,2531,1887,2957,3350,3545,2723,2432,1914,1243,2763,2985,2227,1576,3249,1441,2020,3513,2886,1359,3140,1724,2067,1529,2136,1904,1518,1265,1482,1254,3688,2869,1409,3221,1709,2603,1792,3275,2667,2755,3821,3653,3485,1279,2897,1462,2654,1628,3195,3029,2735,2814,1985,1760,1660,1298,2682,3125,2185,3280,2562,3089,2466,2126,1922,2713,2552,1704,1609,2373,3470,2730,2989,1875,2533,3258,1847,3788,1545,2420,1892,1379,3385,2169,3638,1514,1741,3084,3312,1568,3657,1931,1641,3708,2301,1494,2456,3322,3524,1714,3199,3393,3295,2893,2880,3771,2017,2950,2237,1302,2794,2105,3075,1811,1450,3670,2259,1418,3453,2451,3527,3473,3438,1864,2925,1978,2291,2254,3569,2540,2034,1960,2555,3300,3093,1581,2335,2777,3152,3712,2772,1351,2750,2804,1600,2718,1975,3378,1843,2058,2367,2437,3068,1377,3739,2281,1896,3421,1447,2483,3505,3685,3808,1796,1622,2424,1526,3676,2799,2639,3327,1433,3226,1943,3588,1242,3559,3606,1521,3184,2586,2982,1863,2954,1604,3265,2118,1470,1868,3795,2011,3097,3582,3229,3450,3503,3459,3591,2910,3301,2204,2574,1438,3720,3635,2364,2164,1783,2737,2232,2307,3054,2083,1736,2496,2790,3550,2000,1636,3037,3679,2264,2601,3603,1676,3610,3371,2606,3814,2528,2441,2673,2589,3735,1387,1900,1343,2560,1519,2596,1217,2147,3239,3069,1824,1619,2890,2414,3207,2396,3339,3778,1238,2015,3286,1883,3269,1365,2477,3578,1951,3718,2609,2179,3144,1787,1656,3028,1281,1634,1910,1573,3445,3282,2958,3307,3166,2445,3191,1938,1968,3090,1555,2332,2826,3314,2820,3137,3499,3065,3750,3600,1457,1819,1624,2327,2213,2492,2547,2344,1936,3467,2498,1983,2801,1804,2841,3381,1425,2858,3078,3650,3237,3205,2840,2115,3482,3254,2100,3413,1270,1772,3122,2946,1534,1794,1953,2685,2359,2973,2709,1970,1227,3218,1856,2692,1498,1587,2509,3704,1540,3518,2726,2631,3632,3119,3746,3060,3176,3087,1397,1329,2877,1361,3000,2830,3728,3596,3723,2781,2460,2798,1683,1292,3622,3407,3210,3441,3010,1414,2196,2613,3032,3194,2349,1889,3555,1644,1612,2649,2978,2472,2317,3294,1744,3242,1263,2304,1382,2487,3743,2355,2581,2006,2566,1947,1393,3703,1825,2968,2932,3486,1478,2519,2536,3541,2387,1831,1231,2153,2900,1552,2851,2243,2505,3819,3628,1874,3115,1429,3247,3409,2862,2052,1246,1979,3005,2272,3364,2370,3215,1525,3755,3824,3802,3225,2702,2208,1695,2883,1563,2748,2915,3508,2645,2617,3476,1333,1991,2788,1318,2963,1286,2408,2089,3190,1515,2221,2338,1996,3675,1906,2001,1251,1754,1698,3491,1273,1747,1927,3262,3289,3792,3111,2524,1631,3158,2121,2235,2144,2936,1648,3707,1727,2677,2176,2391,2904,3358,2149,2028,1595,2894,1374,3536,3070,2970,3768,3519,2188,2489,2991,2716,1965,2817,2134,3741,3547,1833,2048,2938,2225,1884,1615,1389,3255,3811,3240,3609,2849,2393,1752,1652,3081,3758,1929,3283,3266,2514,2568,1403,3458,1701,2398,1488,2695,1256,3223,3773,2029,2293,3726,1312,3695,3663,1239,3436,3783,2706,3416,1258,3304,1356,3796,1503,3023,1669,2193,1786,3002,1733,1765,3619,3579,2557,3641,3091,1464,3355,1224,2521,3352,3251,2422,2669,3710,1801,2856,1307,2361,2311,3631,2538,1853,2151,2642,3155,2229,2084,2214,2383,3764,1894,2987,1574,1806,3683,1524,2906,3419,1349,2097,3270,3732,2284,1933,2257,1589,2246,1492,1603,3106,3468,2378,1690,3066,3586,1571,2871,1439,2182,1877,1339,3133,2111,1993,2267,3572,2757,3192,2785,3583,2278,2928,2329,2710,3456,1667,2025,2812,2314,2625,1821,1731,3800,3034,2410,2923,1838,1325,3298,2874,2542,2289,2647,2252,2664,2461,2974,2578,1688,3480,2171,2835,3110,3142,1496,3178,2693,2506,3539,2075,2418,1396,2439,2401,1699,2051,2765,3423,2550,1245,2481,1445,2620,2139,3687,2064,3674,2244,2752,2633,2022,3363,3310,3348,2156,2069,2867,1626,2054,1583,1662,2665,3395,3293,2037,2503,1277,3146,2629,2684,3455,1958,3292,3444,2239,1758,2107,1467,2994,3161,3672,1420,2449,1509,2846,2564,2942,1845,1598,3112,2661,2375,3260,3659,2678,1780,2720,1547,1748,1798,2298,3391,3737,3376,2060,1743,2732,1252,3462,2386,3786,1267,2569,3642,2092,3063,3722,3344,3544,3564,1579,3715,2656,1711,1499,1987,1716,2454,2165,3818,1813,1300,1452,3691,2688,3273,3334,3791,3026,2429,3655,1235,2276,3801,2128,3774,1763,1658,2322,2701,2599,3329,3174,1738,3041,3095,2468,1220,1898,2113,1981,1284,1585,3024,1372,3520,3007,3398,3288,1617,2675,2056,1934,2948,3697,3488,2500,1543,3107,2357,1955,1485,1972,2320,3224,1427,3388,1504,3117,2860,2728,1717,2807,3156,3433,3139,2479,3565,2696,2078,2325,1781,3625,2792,3168,1940,2435,2760,2013,3400,1459,2045,1685,2885,1949,2828,3171,2960,3533,3447,3188,2194,2347,1654,2743,2997,3320,1390,1289,3056,1866,2775,3665,3039,1998,3797,3593,3729,3613,1341,2406,3501,3252,3085,3465,2591,1646,2443,2594,1721,2167,2273,2174,2389,1476,1674,2855,1639,2853,3825,3369,2823,3748,3630,3561,3235,2431,3516,1523,3331,3368,3662,2526,2416,1558,2934,2262,2944,1861,1491,2081,3324,2796,3497,3598,2576,1706,2162,2680,3351,2902,2095,2494,3761,3552,3181,2384,2475,3694,3430,1777,3149,2330,2230,2036,1309,3645,2287,2102,2517,3705,3232,2719,3733,3100,3521,2008,3496,1908,2003,3379,2218,2930,2123,1512,1774,2385,1678,3511,1229,3601,3373,1593,3790,3337,1248,2050,2768,3690,1480,3203,3062,3469,3164,3015,1363,1816,2334,3277,3558,2746,1789,1288,3765,2040,1346,2783,3309,3822,2636,1436,1859,2201,1989,1335,1693,2572,1561,2704,2913,2404,3196,3426,2223,1473,3633,3805,2651,2353,1827,2966,3360,2583,2507,3538,3341,2502,2241,2159,3362,2810,3128,1829,3057,1532,1384,3411,2485,1537,3817,3245,3020,2864,3740,1880,1431,3076,1902,2699,3494,1399,2270,1621,1962,3626,3212,2206,2832,1416,2087,3753,3013,1331,1606,3580,1320,1944,1367,1681,2887,3405,2690,1565,2615,1769,1917,2834,2351,3200,2191,3047,2470,1912,2980,3575,1870,3669,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG380-1 : 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
% 0.14/0.39 % Computer : n009.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 21:56:14 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.10/1.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.17/1.76 % [INFO] Parsing done (658ms).
% 3.17/1.78 % [INFO] Running in sequential loop mode.
% 4.47/2.11 % [INFO] eprover registered as external prover.
% 4.47/2.11 % [INFO] Scanning for conjecture ...
% 5.34/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 1215 axioms. Running axiom selection ...
% 7.22/2.76 % [INFO] Axiom selection finished. Selected 1215 axioms (removed 0 axioms).
% 9.62/3.23 % [INFO] Problem is propositional (TPTP CNF).
% 9.62/3.27 % [INFO] Type checking passed.
% 9.62/3.27 % [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 ...
% 32.50/8.39 % External prover 'e' found a proof!
% 32.50/8.39 % [INFO] Killing All external provers ...
% 32.50/8.39 % Time passed: 7847ms (effective reasoning time: 6610ms)
% 32.85/8.41 % Axioms used in derivation (1215): cls_abs__le__zero__iff_0, cls_divide__le__eq__number__of1_9, cls_norm__add__less_0, cls_divide__le__eq__number__of_9, cls_cos__diff_0, cls_xt1_I9_J_0, cls_le__divide__eq_8, cls_linorder__antisym__conv2_1, cls_norm__diff__triangle__ineq_0, cls_add__pos__nonneg_0, cls_cos__30_0, cls_mult__numeral__1__right_0, clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if, cls_sin__le__one_0, cls_sum__power2__gt__zero__iff_2, cls_le__divide__eq_3, cls_order__le__less__trans_0, cls_less__divide__eq_3, cls_not__one__less__zero_0, clsarity_Int__Oint__HOL_Oeq, cls_mult__less__cancel__left__disj_5, cls_less__iff__diff__less__0_0, cls_real__mult__is__one_1, cls_add__0__left_0, cls_sin__two__pi_0, cls_divide__eq__eq_3, cls_eq__add__iff2_1, cls_norm__sgn_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_mult__zero__right_0, cls_zero__less__one_0, cls_divide__le__eq_2, cls_order__eq__iff_0, cls_comm__semiring__class_Odistrib_0, cls_real__le__add__half__cancel_0, cls_zero__less__divide__iff_5, cls_divide__eq__eq__number__of_4, cls_less__divide__eq__number__of1_6, cls_abs__div__pos_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs, cls_real__sqrt__sum__squares__less_0, cls_mult__imp__le__div__pos_0, cls_divide__pos__pos_0, clsarity_Int__Oint__Int_Onumber, clsarity_RealDef__Oreal__Orderings_Opreorder, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, cls_mult__2__right_0, cls_power2__eq__imp__eq_0, cls_eq__divide__eq__number__of1_4, 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_DERIV__mult__lemma_0, cls_order__less__le__trans_0, cls_divide__less__0__iff_0, clsarity_RealDef__Oreal__RealVector_Oreal__field, cls_not__iszero__1_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_abs__of__nonneg_0, cls_real__mult__le__cancel__iff1_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, cls_real__sum__squares__cancel_0, cls_of__real__power_0, clsarity_Int__Oint__Ring__and__Field_Oabs__if, clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1, cls_divide__le__eq__number__of_4, cls_sin__45_0, cls_number__of__Bit1_0, cls_norm__zero_0, cls_sin__cos__squared__add2__mult_0, cls_mult_Odiff__left_0, clsarity_Int__Oint__Ring__and__Field_Olordered__ring, cls_real__mult__assoc_0, cls_inverse__zero__imp__zero_0, cls_xt1_I12_J_0, cls_divide__self_0, cls_real__sqrt__zero_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_zero__less__norm__iff_1, cls_negative__imp__inverse__negative_0, cls_tan__double_0, cls_eq__divide__2__times__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_sgn__times_0, cls_Bit0__Pls_0, clsarity_Complex__Ocomplex__Int_Onumber, cls_divide__nonpos__neg_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_real__mult__le__cancel__iff2_1, cls_le__divide__eq__number__of1_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_real__0__le__divide__iff_0, cls_comp__arith_I112_J_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_not__iszero__Numeral1_0, cls_half_0, cls_add__increasing2_0, cls_divide__numeral__1_0, cls_less__half__sum_0, cls_abs__diff__triangle__ineq_0, cls_real__sqrt__ge__abs2_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_power2__less__0_0, cls_real__sqrt__mult__self__sum__ge__zero_0, cls_power3__eq__cube_0, cls_diff__add__cancel_0, cls_zero__le__divide__iff_2, cls_iszero__number__of__Bit0_0, cls_inverse__eq__iff__eq_0, cls_power__inject__exp_0, cls_zero__le__mult__iff_3, cls_class__semiring_Osemiring__rules_I29_J_0, cls_abs__triangle__ineq2_0, cls_tan__zero_0, cls_linorder__neqE_0, cls_real__sqrt__gt__0__iff_1, cls_divide__1_0, cls_add__strict__right__mono_0, clsarity_Int__Oint__Orderings_Oorder, cls_divide__less__eq__number__of1_5, cls_real__sqrt__pow2_0, cls_inverse__le__1__iff_2, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, cls_divide__le__eq__number__of1_4, clsarity_Int__Oint__Ring__and__Field_Opordered__ring, cls_le__divide__eq__number__of_6, clsarity_RealDef__Oreal__HOL_Oeq, cls_less__divide__eq__number__of_8, cls_nonzero__inverse__eq__divide_0, clsarity_Int__Oint__OrderedGroup_Omonoid__add, cls_right__distrib__number__of_0, cls_not__sum__squares__lt__zero_0, cls_cos__is__zero_2, clsarity_Int__Oint__Ring__and__Field_Osemiring, cls_class__semiring_Osemiring__rules_I20_J_0, cls_pos__add__strict_0, cls_abs__add__one__gt__zero_0, cls_power__le__zero__eq_3, cls_half__gt__zero_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_of__real__divide_0, cls_add__imp__eq_0, cls_divide__le__eq_7, cls_norm__triangle__ineq4_0, cls_frac__le_0, cls_left__distrib__number__of_0, cls_add__le__cancel__right_1, cls_one__le__inverse__iff_2, cls_sgn0_0, cls_power2__diff_0, cls_number__of__Pls_0, cls_divide__less__eq_4, cls_zero__less__divide__iff_0, cls_abs__eq__mult_1, cls_add__le__cancel__left_1, cls_divide__le__eq_8, cls_real__sqrt__sum__squares__ge__zero_0, cls_real__le__trans_0, cls_Rational_Oordered__idom__class_Osgn__greater_1, cls_sin__cos__squared__add2_0, cls_less__divide__eq__number__of_3, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1, cls_real__0__le__divide__iff_4, cls_divide__less__eq__number__of1_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_tan__45_0, cls_realpow__two__sum__zero__iff_1, cls_divide__less__eq__number__of_1, cls_less__imp__inverse__less__neg_0, cls_real__minus__half__eq_0, cls_rcis__mult_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_of__real__0_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_le__divide__eq__number__of1_5, cls_abs__mult__less_0, cls_divide__le__0__1__iff_1, cls_real__sqrt__lt__0__iff_1, cls_real__le__eq__diff_1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, cls_real__mult__less__iff1_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring, cls_divide__Numeral0_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_realpow__two__le__add__order_0, cls_divide__Numeral1_0, cls_inverse__less__1__iff_2, cls_inverse__1_0, cls_real__sqrt__pow2__gt__zero_0, cls_inverse__negative__iff__negative_1, clsarity_nat__Orderings_Olinorder, cls_mult__nonpos__nonpos_0, cls_real__sqrt__sum__squares__triangle__ineq_0, cls_mult__less__imp__less__right_0, cls_left__inverse_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_real__sqrt__ge__abs1_0, cls_eq__int__code_I14_J_0, cls_add__cancel__21_1, cls_eq__int__code_I9_J_0, cls_left__diff__distrib__number__of_0, cls_cos__two__pi_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs, cls_le__real__sqrt__sumsq_0, cls_lemma__MVT_0, cls_mult__le__cancel__left__pos_0, cls_sin__30_0, cls_eq__divide__eq__number__of_4, cls_cos__le__one_0, cls_divide__eq__eq_0, cls_class__ringb_Onoteq__reduce_0, cls_rel__simps_I49_J_0, cls_comm__monoid__add_Omult__1__right_0, cls_pi__not__less__zero_0, cls_sum__squares__ge__zero_0, cls_power__one_0, cls_abs__cos__le__one_0, cls_add__nonpos__neg_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, cls_abs__of__pos_0, cls_divide__less__eq_5, cls_real__gt__half__sum_0, cls_eq__divide__eq__number__of_1, cls_zero__eq__power2_0, cls_real__mult__le__cancel__iff2_0, cls_divide__less__eq__number__of1_6, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_split__mult__neg__le_0, cls_divide__le__0__iff_3, cls_cos__periodic_0, cls_less__divide__eq_4, cls_real__sqrt__le__1__iff_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, 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cls_le__divide__eq_0, cls_le__divide__eq_6, cls_abs__sin__le__one_0, cls_mult__left__le__one__le_0, cls_add__nonpos__nonpos_0, cls_divide__pos__neg_0, cls_one__less__inverse__iff_2, cls_le__divide__eq__number__of_1, cls_add__nonneg__eq__0__iff_1, cls_sum__power2__eq__zero__iff_1, cls_class__semiring_Osemiring__rules_I3_J_0, cls_one__le__inverse__iff_0, cls_mult__eq__0__iff_2, clsarity_Int__Oint__Orderings_Opreorder, cls_pi__half__le__two_0, cls_order__neq__le__trans_0, cls_real__sgn__def_1, cls_divide__eq__eq__number__of_1, cls_cos__is__zero_1, cls_cos__double_0, cls_class__ringb_Oadd__r0__iff_0, cls_less__divide__eq__number__of_6, cls_power2__abs_0, cls_sin__gt__zero2_0, cls_sum__squares__gt__zero__iff_1, cls_eq__divide__eq_2, cls_tan__periodic_0, cls_add__nonneg__nonneg_0, clsarity_nat__Ring__and__Field_Osemiring, cls_sin__pi_0, cls_mult__mono_H_0, clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs, cls_mult__strict__left__mono__comm_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_abs__mult__self_0, cls_mult__less__cancel__left__neg_1, cls_order__antisym__conv_0, cls_add__numeral__0_0, clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors, cls_divide_Odiff_0, cls_even__less__0__iff_1, cls_division__ring__inverse__add_0, cls_less__divide__eq__number__of1_8, cls_divide__less__eq_2, cls_abs__number__of_1, cls_divide__less__0__1__iff_0, cls_right__diff__distrib__number__of_0, cls_norm__number__of_0, cls_not__real__square__gt__zero_1, cls_linorder__less__linear_0, clsarity_nat__Power_Opower, cls_rel__simps_I51_J_0, cls_inverse__negative__iff__negative_0, cls_cos__double__less__one_0, cls_divide__strict__right__mono__neg_0, cls_abs__not__less__zero_0, cls_add__strict__increasing_0, cls_real__sqrt__le__iff_0, cls_divide__le__eq__number__of_7, cls_abs__le__mult_0, cls_le__divide__eq__number__of_5, cls_le__divide__eq__number__of1_7, clsarity_Int__Oint__Power_Opower, cls_cis__rcis__eq_0, cls_zero__le__mult__iff_5, cls_divide__le__eq_5, cls_nonzero__inverse__inverse__eq_0, cls_power__mult__distrib_0, cls_divide__le__eq__number__of_2, cls_abs__mult__pos_0, cls_lemma__tan__add1_0, cls_eq__divide__imp_0, cls_class__semiring_Osemiring__rules_I11_J_0, clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring, cls_eq__eqI_0, clsarity_RealDef__Oreal__Ring__and__Field_Ofield, cls_sum__power2__le__zero__iff_0, cls_order__less__le_2, cls_mult__less__cancel__left__pos_1, cls_real__sqrt__abs_0, clsarity_Int__Oint__Int_Onumber__ring, cls_pi__neq__zero_0, cls_real__sqrt__one_0, cls_eq__divide__eq__number__of_2, cls_nonzero__inverse__eq__imp__eq_0, cls_cos__zero_0, cls_zero__le__mult__iff_1, clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add, cls_power__commutes_0, cls_iszero__def_0, cls_divide__eq__eq__number__of1_4, cls_xt1_I11_J_0, cls_add__neg__neg_0, cls_sin__double_0, cls_norm__mult_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__field, cls_inverse__eq__divide__number__of_0, cls_real__sqrt__gt__1__iff_0, cls_number__of__Bit0_0, cls_le__eqI_0, cls_cos__sin__eq_0, cls_zero__less__power2_1, clsarity_Int__Oint__Ring__and__Field_Osgn__if, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, cls_divide__eq__imp_0, cls_mult__le__cancel__left__neg_0, cls_zero__less__abs__iff_1, cls_divide__less__eq_7, cls_divide__less__eq__number__of_8, cls_abs__if__lattice_1, clsarity_Int__Oint__Ring__and__Field_Oring, cls_abs__divide_0, cls_zero__le__divide__iff_0, cls_cos__gt__zero_0, cls_norm__eq__zero_0, cls_mult__imp__div__pos__less_0, cls_abs__triangle__ineq_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_less__divide__eq__number__of1_4, cls_mult__le__0__iff_2, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_real__0__le__divide__iff_2, cls_divide__less__eq__number__of_3, cls_real__le__antisym_0, cls_divide__less__0__iff_2, cls_real__sq__order_0, cls_divide__left__mono_0, cls_eq__int__code_I15_J_0, cls_mult__1_0, cls_divide__less__0__iff_5, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, cls_comm__monoid__add_Omult__left__commute_0, cls_add__frac__num_0, cls_mult__right__mono__neg_0, cls_abs__mult_0, cls_sgn__sgn_0, cls_real__sqrt__ge__1__iff_1, cls_sum__squares__eq__zero__iff_2, cls_le__divide__eq__number__of1_3, clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict, cls_diff__divide__distrib_0, cls_xt1_I6_J_0, cls_of__real__diff_0, cls_diff__0__right_0, cls_positive__imp__inverse__positive_0, cls_le__add__right__mono_0, cls_inverse__inverse__eq_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_mult__less__cancel__left__disj_3, cls_norm__mult__ineq_0, cls_divide__le__eq__number__of1_1, cls_cos__squared__eq_0, cls_zero__less__mult__pos2_0, cls_divide__eq__eq__number__of1_1, clsarity_Int__Oint__OrderedGroup_Omonoid__mult, cls_mult_Oadd__right_0, clsarity_nat__HOL_Oeq, cls_cos__x__y__le__one_0, cls_mult__less__cancel__right__disj_4, cls_mult__1__left_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring, cls_rabs__ratiotest__lemma_0, cls_zero__le__divide__1__iff_1, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add, cls_frac__eq__eq_1, cls_norm__le__zero__iff_1, cls_cos__monotone__0__pi_0, cls_sin__zero__abs__cos__one_0, cls_pi__half__neq__zero_0, clsarity_nat__Ring__and__Field_Omult__mono1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors, cls_eq__add__iff2_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_real__sqrt__le__1__iff_1, cls_one__less__inverse__iff_0, cls_sin__60_0, cls_real__sum__square__gt__zero2_0, cls_zero__less__divide__1__iff_1, cls_inverse__less__1__iff_1, cls_power2__eq__square__number__of_0, cls_abs__triangle__ineq3_0, cls_Rational_Oordered__idom__class_Osgn__greater_0, cls_mult__zero__left_0, cls_real__zero__not__eq__one_0, cls_comm__monoid__add_Omult__1_0, cls_of__real__eq__iff_0, cls_divide__le__0__iff_4, cls_linorder__not__le_0, cls_eq__int__code_I1_J_0, cls_real__sqrt__eq__1__iff_0, cls_sin__cos__eq_0, cls_norm__mult__less_0, clsarity_Int__Oint__Ring__and__Field_Oidom, cls_le__divide__eq_9, cls_real__add__mult__distrib_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_le__divide__eq_4, cls_class__semiring_Oadd__c_0, cls_less__divide__eq_6, cls_rel__simps_I44_J_0, cls_mult__left__le__imp__le_0, clsarity_Complex__Ocomplex__HOL_Oeq, cls_real__sqrt__gt__0__iff_0, cls_divide__less__0__iff_1, cls_order__less__irrefl_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field, cls_norm__of__real_0, cls_frac__less2_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_gt__half__sum_0, cls_divide__less__eq__number__of_9, cls_divide__le__eq__number__of1_3, cls_one__less__inverse__iff_1, cls_real__mult__1_0, cls_power2__eq__square_0, cls_add__nonneg__eq__0__iff_2, cls_diff__frac__eq_0, cls_power__eq__0__iff_0, cls_eq__eqI_1, cls_abs__sgn_0, cls_nonzero__power__divide_0, cls_divide__le__eq__number__of1_8, clsarity_Int__Oint__OrderedGroup_Oab__group__add, cls_mult__pos__pos_0, cls_less__eqI_0, clsarity_Int__Oint__Ring__and__Field_Omult__mono1, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_class__fieldgb_Odivide__inverse_0, cls_real__sum__squares__cancel2_0, cls_real__sqrt__two__gt__one_0, cls_inverse__less__imp__less__neg_0, cls_complex__mod__rcis_0, cls_divide_Oadd_0, cls_mult__right__less__imp__less_0, clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add, cls_tan__inverse_0, cls_sum__squares__gt__zero__iff_0, cls_inverse__le__imp__le_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring, cls_mult_Oprod__diff__prod_0, cls_class__semiring_Osemiring__rules_I8_J_0, cls_real__sqrt__divide_0, cls_divide__less__eq__number__of1_4, cls_inverse__zero_0, cls_cos__60_0, cls_le__divide__eq__number__of1_1, cls_norm__ratiotest__lemma_0, cls_zero__less__divide__iff_4, cls_inverse__eq__divide_0, cls_real__sqrt__sum__squares__mult__squared__eq_0, cls_add__pos__pos_0, cls_rcis__zero__arg_0, cls_power__less__imp__less__base_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom, cls_cos__3over2__pi_0, cls_add__mono_0, cls_divide__le__0__iff_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add, cls_sgn__one_0, cls_less__divide__eq__number__of_2, cls_sgn__1__pos_0, cls_sgn__mult_0, cls_of__real__number__of__eq_0, cls_cos__one__sin__zero_0, cls_real__sqrt__eq__zero__cancel_0, cls_divide__less__eq_9, cls_add__neg__nonpos_0, clsarity_Complex__Ocomplex__Power_Opower, cls_eq__divide__eq__number__of1_0, cls_mult__divide__mult__cancel__right_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add, cls_iszero__number__of__Bit0_1, cls_class__semiring_Osemiring__rules_I24_J_0, cls_divide__le__eq_9, cls_eq__iff__diff__eq__0_1, clsarity_RealDef__Oreal__Orderings_Oorder, cls_add__less__cancel__left_0, cls_divide__strict__right__mono_0, cls_abs__inverse_0, cls_divide__less__eq_6, cls_real__0__le__divide__iff_1, cls_mult__less__cancel__left__disj_2, cls_power__eq__0__iff__number__of_0, cls_frac__less_0, cls_real__mult__commute_0, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult, cls_real__mult__le__cancel__iff1_1, clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_field__inverse_0, cls_cos__is__zero_3, cls_divide__inverse_0, cls_class__semiring_Opwr__mul_0, cls_abs__le__zero__iff_1, cls_abs__eq__0_1, cls_mult__less__cancel__right__disj_1, cls_real__sqrt__le__0__iff_1, cls_class__ringb_Osubr0__iff_1, cls_two__realpow__ge__one_0, cls_abs__one_0, cls_real__sgn__eq_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_less__divide__eq__number__of1_9, cls_inverse__mult__distrib_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring, cls_less__divide__eq_0, cls_divide__less__eq__number__of_2, cls_sum__power2__eq__zero__iff_2, cls_add__tan__eq_0, cls_divide__eq__eq__number__of_2, cls_sin__periodic_0, cls_eq__divide__eq__number__of_0, cls_le__eqI_1, cls_power2__sum_0, cls_mult__eq__0__iff_1, cls_le__iff__diff__le__0_1, cls_divide__nonpos__pos_0, cls_add__less__le__mono_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add, cls_norm__le__zero__iff_0, cls_lemma__real__divide__sqrt__less_0, cls_zero__le__power_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom, cls_divide__less__eq_3, cls_sgn__if_1, clsarity_nat__Ring__and__Field_Osemiring__1, cls_nonzero__inverse__mult__distrib_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_nonzero__power__inverse_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, cls_inverse__less__imp__less_0, cls_order__less__imp__le_0, cls_abs__le__D1_0, cls_le__divide__eq__number__of1_4, cls_real__sqrt__sum__squares__eq__cancel2_0, clsarity_Complex__Ocomplex__RealVector_Oreal__field, cls_real__less__def_2, cls_realpow__two__le__add__order2_0, cls_abs__eq__mult_2, cls_not__real__square__gt__zero_0, cls_cos__pi__half_0, cls_inverse__positive__imp__positive_0, clsarity_Int__Oint__Ring__and__Field_Osemiring__1, cls_real__le__eq__diff_0, cls_le__imp__inverse__le__neg_0, cls_less__divide__eq__number__of_5, cls_division__ring__inverse__diff_0, cls_le__divide__eq__number__of_4, cls_zero__le__divide__iff_1, cls_cos__two__less__zero_0, cls_tan__gt__zero_0, cls_divide__less__eq__number__of1_1, cls_rcis__def_0, cls_norm__diff__ineq_0, cls_mult__idem_0, cls_monoid__add__class_Oadd__0__right_0, cls_real__sqrt__lt__0__iff_0, cls_sin__diff2_0, cls_cos__add_0, cls_add__strict__increasing2_0, clsarity_RealDef__Oreal__Int_Onumber__ring, clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_real__0__le__divide__iff_5, cls_class__ringb_Osubr0__iff_0, cls_realpow__two__sum__zero__iff_2, cls_divide__le__eq__number__of1_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_eq__iff__diff__eq__0_0, cls_inverse__numeral__1_0, cls_zero__less__norm__iff_0, cls_inverse__nonpositive__iff__nonpositive_1, cls_sin__diff_0, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_real__sqrt__sum__squares__mult__ge__zero_0, cls_divide__less__0__1__iff_1, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring, cls_le__divide__eq__number__of1_8, cls_power__Suc__less_0, cls_less__eqI_1, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_add__numeral__0__right_0, cls_xt1_I7_J_0, cls_real__sqrt__not__eq__zero_0, cls_mult__neg__neg_0, cls_linorder__not__less_1, 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_zero__le__power2_0, cls_mult__less__le__imp__less_0, cls_less__divide__eq__number__of1_5, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, cls_rel__simps_I48_J_0, cls_rcis__def__raw_0, cls_cos__is__zero_0, cls_divide__less__eq__number__of_5, cls_real__sqrt__power_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_tan__60_0, cls_even__less__0__iff_0, cls_power__le__zero__eq__number__of_3, cls_le__divide__eq__number__of_0, cls_mult__less__cancel__left__pos_0, cls_split__mult__neg__le_1, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1, cls_power__mono_0, cls_abs__power2_0, cls_divide__le__eq_1, cls_mult__left_Oadd_0, cls_comp__arith_I110_J_0, cls_rel__simps_I46_J_0, cls_divide__le__eq__number__of_3, clsarity_Int__Oint__Ring__and__Field_Oordered__idom, cls_le__divide__eq__number__of_9, cls_eq__int__code_I4_J_0, cls_sum__squares__le__zero__iff_0, cls_less__divide__eq__number__of_9, cls_abs__triangle__ineq4_0, cls_real__sqrt__ge__0__iff_0, cls_iszero__0_0, cls_norm__divide_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_real__sqrt__two__ge__zero_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs, cls_divide__less__0__iff_4, cls_nonzero__of__real__divide_0, cls_Deriv_Oadd__diff__add_0, cls_real__mult__self__sum__ge__zero_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_real__sqrt__le__iff_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1, cls_cos__monotone__0__pi_H_0, cls_divide__le__eq__number__of_6, cls_less__divide__eq__number__of1_1, cls_abs__diff__less__iff_0, cls_zero__le__mult__iff_2, cls_divide__le__0__1__iff_0, cls_abs__le__interval__iff_1
% 32.85/8.42 % No. of inferences in proof: 2433
% 32.85/8.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 7847 ms resp. 6610 ms w/o parsing
% 36.10/9.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.27/9.20 % [INFO] Killing All external provers ...
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