%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV716-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 09:00:17 AM UTC 2026
% Result : Unsatisfiable 84.33s 19.55s
% Output : Refutation 88.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1568
% Syntax : Number of formulae : 3137 ( 587 unt; 0 typ; 0 def)
% Number of atoms : 8925 (1828 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 58306 (5270 ~;5788 |; 0 &;47248 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 100 usr; 11 con; 0-6 aty)
% Number of variables : 8480 ( 0 ^;8480 !; 0 ?;8480 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(v_i_____decl,type,
v_i____: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $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(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(v_ka_____decl,type,
v_ka____: $i ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_FFT__Mirabelle_OIDFT_decl,type,
c_FFT__Mirabelle_OIDFT: $i > $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(c_HOL_Oinverse__class_Odivide_decl,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(c_FFT__Mirabelle_Oroot_decl,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i ).
thf(c_FFT__Mirabelle_OIFFT_decl,type,
c_FFT__Mirabelle_OIFFT: $i > $i > $i ).
thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(class_OrderedGroup_Opordered__ab__group__add__abs_decl,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oabs__class_Oabs_decl,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Oabs__if_decl,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring__abs_decl,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $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_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
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(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Divides_Odiv__class_Odiv_decl,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $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(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $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_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_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $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(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_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Int_OMin_decl,type,
c_Int_OMin: $i ).
thf(class_Ring__and__Field_Oring__1_decl,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_Fact_Ofact__class_Ofact_decl,type,
c_Fact_Ofact__class_Ofact: $i > $i > $i ).
thf(class_Ring__and__Field_Olordered__ring_decl,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_Parity_Oeven__odd__class_Oeven_decl,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_decl,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_decl,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $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_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(class_Int_Oring__char__0_decl,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $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_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Omult__mono_decl,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Groebner__Basis_Ogb__semiring_decl,type,
c_Groebner__Basis_Ogb__semiring: $i > $i > $i > $i > $i > $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Complex_Oii_decl,type,
c_Complex_Oii: $i ).
thf(class_RealVector_Oreal__field_decl,type,
class_RealVector_Oreal__field: $i > $o ).
thf(261,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(2163,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1545,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(5116,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1545]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(701,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq__number__of_0) ).
thf(3167,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(375,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/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
thf(2412,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)],[375]) ).
thf(431,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(2544,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[431]) ).
thf(1027,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(3927,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(1352,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(4682,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(1438,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_OIDFT ) ) )
= ( B @ ( A @ ( v_ka____ @ c_FFT__Mirabelle_OIFFT ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc_Ohyps_0) ).
thf(4877,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_OIDFT ) ) )
= ( B @ ( A @ ( v_ka____ @ c_FFT__Mirabelle_OIFFT ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(169,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Parity_Oeven__odd__class_Oeven ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
thf(1950,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Parity_Oeven__odd__class_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(301,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
thf(2250,plain,
tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(2199,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(638,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(3021,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)],[638]) ).
thf(550,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).
thf(2822,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1141,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__div__two__times__two_0) ).
thf(4188,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(9,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oabs__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).
thf(1586,plain,
tc_Int_Oint @ class_Ring__and__Field_Oabs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(4201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(2452,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(1301,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(4560,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1879,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)],[139]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(2612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(1101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(4094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[1101]) ).
thf(1531,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
thf(5088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1531]) ).
thf(516,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__number__of_0) ).
thf(2744,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(578,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_2) ).
thf(2889,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(2306,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(653,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(3053,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1255,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(4450,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(776,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_0) ).
thf(3345,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(1060,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).
thf(4005,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1060]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(2341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1415,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/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(4824,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)],[1415]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( 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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(2131,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( 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)],[246]) ).
thf(1453,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(4909,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(1170,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).
thf(4262,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1170]) ).
thf(93,axiom,
~ ( tc_Int_Oint @ ( c_Int_OMin @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I7_J_0) ).
thf(1767,plain,
~ ( tc_Int_Oint @ ( c_Int_OMin @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(1995,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)],[190]) ).
thf(1028,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(3930,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1133,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(4169,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(1068,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
thf(4022,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(1729,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(833,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(3477,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1050,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(3979,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(877,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(3581,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(1427,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2__right_0) ).
thf(4852,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(534,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(2787,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(1850,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)],[126]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(2499,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1045,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).
thf(3969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1045]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(1982,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[184]) ).
thf(871,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
thf(3566,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(1374,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_2) ).
thf(4728,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(317,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 ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).
thf(2280,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 ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1451,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(4904,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(703,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(3172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(2077,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[223]) ).
thf(1054,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div__lemma_0) ).
thf(3990,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(140,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1882,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_1) ).
thf(2622,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1192,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/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(4311,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)],[1192]) ).
thf(360,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(2381,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(609,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel2_0) ).
thf(2953,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(485,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( E @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).
thf(2671,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( E @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1366,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(4711,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(1152,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).
thf(4215,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_1) ).
thf(4408,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(1314,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/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(4592,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)],[1314]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(1750,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[86]) ).
thf(708,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
thf(3185,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(1367,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__special_I2_J_0) ).
thf(4714,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(1075,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mod__eq__add3__mod__number__of_0) ).
thf(4037,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(602,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(2940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(14,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).
thf(1596,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1490,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/sandbox2/benchmark/theBenchmark.p',cls_divide__numeral__1_0) ).
thf(5000,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)],[1490]) ).
thf(806,axiom,
tc_nat @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(3417,plain,
tc_nat @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
thf(2527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(646,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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).
thf(3040,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)],[646]) ).
thf(1227,axiom,
tc_nat @ ( v_ka____ @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_i_0) ).
thf(4391,plain,
tc_nat @ ( v_ka____ @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(825,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(3460,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(1,negated_conjecture,
tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1569,plain,
tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(1407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).
thf(4807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1407]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(1939,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(4697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(238,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(2114,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[238]) ).
thf(556,axiom,
! [A: $i] :
( ( A @ ( A @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
thf(2837,plain,
! [A: $i] :
( ( A @ ( A @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1971,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(104,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 @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(1793,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 @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(4614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(792,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I37_J_0) ).
thf(3382,plain,
c_Int_OPls != c_Int_OMin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1267,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(4479,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(1290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(4532,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(1105,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).
thf(4105,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(1655,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)],[41]) ).
thf(949,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(3745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(2686,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(1307,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(4575,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(648,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__inj__on_0) ).
thf(3044,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(599,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_Int_Oint @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__nat__number__of_0) ).
thf(2933,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_Int_Oint @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(894,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(3616,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1303,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(4564,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(584,axiom,
~ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_False_0) ).
thf(2901,plain,
~ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(2575,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(994,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mod_5) ).
thf(3848,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(277,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 ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
thf(2195,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 ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1294,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 @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).
thf(4543,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 @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1294]) ).
thf(1547,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(5120,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(721,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(3217,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = D )
| ( ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(4234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = D )
| ( ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1506,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2_0) ).
thf(5037,plain,
! [A: $i] :
( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
thf(1608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).
thf(4403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1233]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(2035,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(770,axiom,
tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos2_0) ).
thf(3332,plain,
tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1034,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
thf(3942,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(687,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(3135,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(1102,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
thf(4097,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(1441,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arith__simps_I31_J_0) ).
thf(4884,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(785,axiom,
! [A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__power2_0) ).
thf(3365,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(1435,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(4870,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(2740,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(592,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(2918,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1107,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__nat__number__of_0) ).
thf(4110,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1288,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).
thf(4528,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
thf(2184,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)],[271]) ).
thf(704,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).
thf(3175,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
thf(1999,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(818,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(3446,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1333,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(4638,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(1872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1429,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).
thf(4856,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(1250,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(4440,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(1339,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__one__le__power_0) ).
thf(4650,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(264,axiom,
tc_Int_Oint @ class_Divides_Oring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).
thf(2168,plain,
tc_Int_Oint @ class_Divides_Oring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(1919,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)],[157]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(2459,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(5005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(869,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_1) ).
thf(3562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[869]) ).
thf(171,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
thf(1954,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(2844,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[559]) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(2146,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)],[254]) ).
thf(1482,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(4980,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(1013,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(3895,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(936,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I16_J_1) ).
thf(3717,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(787,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(3370,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1080,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
thf(4047,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(861,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__Suc__eq__div__add3_0) ).
thf(3545,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ( ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_nat @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff__rev__if_1) ).
thf(4679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ( ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_nat @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(3088,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(1613,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(760,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_0) ).
thf(3308,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(748,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__less__mono__nat_0) ).
thf(3281,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(2082,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1320,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__m1__even_0) ).
thf(4607,plain,
! [B: $i,A: $i] :
( ( ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(418,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(2516,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[418]) ).
thf(1321,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 @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).
thf(4610,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 @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1321]) ).
thf(886,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(3597,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(989,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_3) ).
thf(3836,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1206,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(4343,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(729,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
thf(3236,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(899,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).
thf(3629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( 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)],[899]) ).
thf(617,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).
thf(2972,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[617]) ).
thf(901,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(3634,plain,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(957,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_1) ).
thf(3766,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).
thf(1914,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)],[154]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
thf(2491,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)],[408]) ).
thf(523,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(2763,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(2548,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
thf(2227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1548,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(5123,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(735,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_4) ).
thf(3249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[735]) ).
thf(1219,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).
thf(4371,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(1095,axiom,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(4079,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(1650,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)],[39]) ).
thf(942,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).
thf(3730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[942]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(1645,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)],[37]) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1921,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)],[158]) ).
thf(689,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(3140,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1118,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(4137,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(2400,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[369]) ).
thf(1475,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).
thf(4963,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1475]) ).
thf(1197,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_1) ).
thf(4322,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(549,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
thf(2819,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1468,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_4) ).
thf(4948,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(2531,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(1262,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(4467,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
thf(2405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(924,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I4_J_1) ).
thf(3688,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1394,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).
thf(4775,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(1280,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__plus__one__div__two_0) ).
thf(4511,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(5024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1628,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)],[29]) ).
thf(741,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power2_0) ).
thf(3263,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(745,axiom,
! [A: $i] :
( ( A = c_Int_OMin )
| ( ( A @ c_Int_OBit1 )
!= c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I47_J_0) ).
thf(3275,plain,
! [A: $i] :
( ( A = c_Int_OMin )
| ( ( A @ c_Int_OBit1 )
!= c_Int_OMin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(680,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(3116,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(775,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( B @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
thf(3342,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( B @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(839,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).
thf(3495,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1156,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__2__cases_0) ).
thf(4224,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(982,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(3821,plain,
tc_nat @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(1519,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(5064,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add1__eq_0) ).
thf(2274,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(961,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(3776,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(997,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(3855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(442,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(2571,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
thf(2603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(591,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_2) ).
thf(2916,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(712,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(3195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1380,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(4743,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(1433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
thf(4866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1433]) ).
thf(103,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(1792,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(511,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(2735,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1242,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( B @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
thf(4422,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( B @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(1760,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)],[90]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
thf(1660,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)],[43]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(3046,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(341,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(2339,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)],[341]) ).
thf(1357,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__if_0) ).
thf(4692,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(1388,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
thf(4761,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(656,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
thf(3061,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1341,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).
thf(4654,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1341]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
thf(2444,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(286,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(2217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(892,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(3612,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(693,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).
thf(3148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[693]) ).
thf(1176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(4275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(4349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(803,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(3410,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
thf(1577,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ 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)],[6]) ).
thf(951,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(3749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
thf(2488,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(1832,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(582,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).
thf(2897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[582]) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
thf(1992,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)],[188]) ).
thf(780,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(3353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
thf(2466,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1540,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(5108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(243,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 @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(2126,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 @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(379,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
thf(2420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(672,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(3099,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(64,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(1704,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1346,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(4664,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(1120,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_1) ).
thf(4141,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(259,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(2158,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1171,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(4265,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(1525,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(5076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1315,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 ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(4595,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 ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(1110,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(4119,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(1057,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__power__nat_0) ).
thf(3998,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(991,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__Suc__Suc__4n__diff__2_0) ).
thf(3840,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(145,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__nonzero__nat_0) ).
thf(1892,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(826,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(3463,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(789,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(3374,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(793,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(3385,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(564,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__Suc__0__nat_0) ).
thf(2857,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1210,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_lessequals ) ) )
| ( A @ ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(4353,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_lessequals ) ) )
| ( A @ ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(1399,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).
thf(4788,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(2169,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)],[265]) ).
thf(903,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_4) ).
thf(3638,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(1143,axiom,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit1__Min_0) ).
thf(4194,plain,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
thf(4358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1213]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1550,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(5127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(1326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(4622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(1023,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(3919,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
thf(4830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1417]) ).
thf(1195,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(4317,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(666,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
thf(3084,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[666]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality_H_0) ).
thf(2635,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(1513,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
thf(5052,plain,
tc_Complex_Ocomplex @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(762,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
thf(3312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[762]) ).
thf(911,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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).
thf(3657,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)],[911]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(1931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(201,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
thf(2024,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(35,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
thf(1641,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(2301,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)],[326]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(1815,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1259,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 @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_0) ).
thf(4460,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 @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[1259]) ).
thf(706,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(3180,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).
thf(4471,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(1278,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( F @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(4507,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( F @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(867,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(3557,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).
thf(1875,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)],[137]) ).
thf(1499,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).
thf(5020,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= 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)],[1499]) ).
thf(888,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(3602,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__ring__1__class_Opower__minus__even_0) ).
thf(2852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(727,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(3231,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(363,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(2388,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1002,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power3__eq__cube_0) ).
thf(3866,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1188,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel1_0) ).
thf(4302,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(1281,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(4514,plain,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(1167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(4253,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1061,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).
thf(4008,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(766,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__eq__power2_0) ).
thf(3322,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(852,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).
thf(3524,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(1425,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq__number__of_1) ).
thf(4847,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(1411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).
thf(4815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1411]) ).
thf(1561,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(5156,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(321,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
thf(2291,plain,
tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
thf(1677,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(2335,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)],[339]) ).
thf(1246,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__ex__iff_1) ).
thf(4432,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(2456,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(288,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(2222,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1237,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(4411,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__le__mono_0) ).
thf(1664,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(537,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 @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(2794,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 @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1010,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(3887,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(1714,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)],[69]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(2027,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1450,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(4903,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(662,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ( ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_nat @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff__rev__if_0) ).
thf(3075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ( ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( tc_nat @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1252,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( F @ ( A @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( E @ ( A @ ( F @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
thf(4443,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( F @ ( A @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( E @ ( A @ ( F @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(1529,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).
thf(5084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1529]) ).
thf(1308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(4578,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1308]) ).
thf(234,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
thf(2105,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1066,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I10_J_1) ).
thf(4018,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(1502,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
thf(5027,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(796,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(3393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).
thf(2996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[627]) ).
thf(940,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(3724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).
thf(1911,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)],[153]) ).
thf(1317,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(4600,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(532,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(2782,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
thf(2893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[580]) ).
thf(1185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(4297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(398,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(2469,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)],[398]) ).
thf(1376,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_1) ).
thf(4733,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(306,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(2259,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)],[306]) ).
thf(699,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(3163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(476,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(2650,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(831,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(3473,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(930,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(3702,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(815,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(3438,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(1123,axiom,
! [A: $i] :
( ( c_Int_OPls = A )
| ( c_Int_OPls
!= ( A @ c_Int_OBit0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).
thf(4147,plain,
! [A: $i] :
( ( c_Int_OPls = A )
| ( c_Int_OPls
!= ( A @ c_Int_OBit0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(1082,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(4050,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(896,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
thf(3621,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1047,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(3973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1047]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[174]) ).
thf(670,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
thf(3093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1553,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__div__cancel_0) ).
thf(5135,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(1403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(4798,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(530,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).
thf(2777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[530]) ).
thf(695,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(3152,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(959,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(3771,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs_0) ).
thf(4162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(613,axiom,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I50_J_0) ).
thf(2964,plain,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
thf(2058,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)],[215]) ).
thf(1073,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(4033,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(2861,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(274,axiom,
tc_Int_Oint @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).
thf(2190,plain,
tc_Int_Oint @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).
thf(4701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1361]) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(2103,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)],[233]) ).
thf(1370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(4718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(1383,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(4751,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(1344,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(4660,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(857,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def2_1) ).
thf(3537,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(1928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1085,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def2_1) ).
thf(4055,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(659,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(3068,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1216,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(4364,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(2371,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(2772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(697,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 @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
thf(3157,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 @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(919,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nat__number__of_0) ).
thf(3676,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
thf(2137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ 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)],[249]) ).
thf(1459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(4924,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1459]) ).
thf(1566,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(5169,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(2002,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)],[193]) ).
thf(544,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(2809,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
thf(2242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(2286,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(2639,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[471]) ).
thf(1554,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_2) ).
thf(5137,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(1364,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(4707,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(881,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(3588,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(868,axiom,
! [A: $i] :
( ( A = c_Int_OPls )
| ( ( A @ c_Int_OBit0 )
!= c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I44_J_0) ).
thf(3559,plain,
! [A: $i] :
( ( A = c_Int_OPls )
| ( ( A @ c_Int_OBit0 )
!= c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1180,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(4285,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1018,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).
thf(3906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1018]) ).
thf(1312,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I8_J_1) ).
thf(4588,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(838,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(3492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(504,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(2718,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(2205,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1696,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(449,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 @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power2_0) ).
thf(2586,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 @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[449]) ).
thf(576,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I36_J_0) ).
thf(2884,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(1269,axiom,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).
thf(4483,plain,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(846,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(3510,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(1863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(998,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(3857,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',cls_abs__divide_0) ).
thf(1691,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)],[59]) ).
thf(1565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(5167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(1505,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(5034,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
thf(1708,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)],[66]) ).
thf(472,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(2641,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(920,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__div__geq_0) ).
thf(3679,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1015,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(3899,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)],[1015]) ).
thf(594,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(2922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[594]) ).
thf(1568,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(5174,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
thf(2011,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)],[196]) ).
thf(878,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(3582,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(726,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(3229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[726]) ).
thf(634,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_0) ).
thf(3011,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(1319,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(4604,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(820,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono__odd_0) ).
thf(3450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(3503,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(1145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).
thf(4199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1445,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(4893,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(1198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(4323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(883,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(3591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(756,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div_H_7) ).
thf(3301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(757,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
thf(3303,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[757]) ).
thf(1384,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(4753,plain,
! [B: $i,A: $i] :
( ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(1235,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(4407,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(1329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(4629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(1289,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( c_Suc @ c_COMBB ) ) ) ) @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__double__inj__on_0) ).
thf(4531,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( c_Suc @ c_COMBB ) ) ) ) @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1497,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
thf(5017,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1497]) ).
thf(902,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ ( F @ ( A @ ( E @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
thf(3635,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ ( F @ ( A @ ( E @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(352,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(2364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1556,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(5142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(1300,axiom,
! [A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_2) ).
thf(4557,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1056,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).
thf(3995,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1056]) ).
thf(210,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
thf(2047,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)],[210]) ).
thf(1094,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(4076,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(512,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(2737,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(293,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
thf(2232,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(324,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
thf(2296,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)],[324]) ).
thf(1072,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(4031,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(79,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 ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(1736,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 ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(4100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(2496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(535,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).
thf(2790,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[535]) ).
thf(1087,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 @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).
thf(4059,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 @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1087]) ).
thf(586,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(2905,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(134,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
thf(1868,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(2061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(863,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(3550,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(1134,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).
thf(4172,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)],[1134]) ).
thf(807,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 @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(3418,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 @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(970,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(3795,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(2441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(944,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( C = D )
| ( ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
thf(3735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( C = D )
| ( ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(2264,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(740,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power2_0) ).
thf(3261,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(985,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).
thf(3827,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)],[985]) ).
thf(430,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__pwr_0) ).
thf(2541,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1221,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).
thf(4375,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[1221]) ).
thf(46,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( 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 ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
thf(1666,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( 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 ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[46]) ).
thf(891,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(3610,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(615,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(2969,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1254,axiom,
tc_Int_Oint @ ( c_Int_OPls @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I6_J_0) ).
thf(4449,plain,
tc_Int_Oint @ ( c_Int_OPls @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(1420,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(4836,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)],[1420]) ).
thf(934,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( B @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
thf(3711,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( B @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(2733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1065,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
thf(4016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1065]) ).
thf(542,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(2805,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(453,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(2596,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1230,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_3) ).
thf(4397,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(1457,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(4920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1457]) ).
thf(7,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(1580,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(315,axiom,
tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
thf(2277,plain,
tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(2,negated_conjecture,
tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(1570,plain,
tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(51,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
thf(1676,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(952,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( 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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_0) ).
thf(3752,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( 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)],[952]) ).
thf(1285,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I12_J_1) ).
thf(4521,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(1114,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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(4128,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)],[1114]) ).
thf(728,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
thf(3233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[728]) ).
thf(1009,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(3884,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(4499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(2606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(1824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(980,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).
thf(3816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[980]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(2032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(4821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1414]) ).
thf(979,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
thf(3814,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(623,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__special_I4_J_1) ).
thf(2986,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1129,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_3) ).
thf(4160,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(1345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
thf(4661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(914,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
thf(3664,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(367,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(2396,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[367]) ).
thf(921,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(3682,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(773,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(3339,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(962,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(3778,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1011,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
thf(3889,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(830,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(3471,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1078,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(4044,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(750,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
thf(3286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[750]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(1883,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1036,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(3948,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(763,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( 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 @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(3314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( 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 @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(876,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= 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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).
thf(3578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= 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)],[876]) ).
thf(458,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(2609,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(2179,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)],[269]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).
thf(2327,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(2211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(956,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) )
= B )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(3763,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) )
= B )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(941,axiom,
! [A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__eq__power2_1) ).
thf(3727,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(915,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_FFT__Mirabelle_OIFFT ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IFFT_Osimps_I1_J_0) ).
thf(3667,plain,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_FFT__Mirabelle_OIFFT ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(972,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__add__num__eq__if2__nat_0) ).
thf(3799,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1070,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(4027,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(478,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
thf(2653,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[478]) ).
thf(1040,axiom,
~ ( tc_Int_Oint @ ( c_Int_OMin @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I3_J_0) ).
thf(3958,plain,
~ ( tc_Int_Oint @ ( c_Int_OMin @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(4295,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(710,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).
thf(3191,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[710]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(2464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).
thf(4280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1178]) ).
thf(521,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(2758,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(571,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
thf(2873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[571]) ).
thf(743,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(3269,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
thf(1602,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)],[18]) ).
thf(895,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_0) ).
thf(3618,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( 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)],[895]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(2628,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(977,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(3810,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1084,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ c_Int_OBit1 @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I9_J_0) ).
thf(4053,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ c_Int_OBit1 @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1311,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).
thf(4585,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[1311]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__minus1_0) ).
thf(2433,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( 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)],[384]) ).
thf(800,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_0) ).
thf(3403,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(177,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
thf(1968,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(713,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(3198,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1488,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
thf(4994,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(1386,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(4757,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)],[1386]) ).
thf(841,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(3499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(778,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(3349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[778]) ).
thf(1225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ( ( tc_nat @ ( D @ ( C @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( tc_nat @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__realpow__diff_0) ).
thf(4385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ( ( tc_nat @ ( D @ ( C @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( tc_nat @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(1951,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(143,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1888,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1006,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono__even_0) ).
thf(3877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(887,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(3600,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)],[887]) ).
thf(56,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(1687,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(219,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(2068,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(115,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(1819,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(691,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 @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).
thf(3144,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 @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[691]) ).
thf(1381,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(4746,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(856,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).
thf(3535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[856]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__mono__nat_0) ).
thf(1787,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1543,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(5113,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
thf(2181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[270]) ).
thf(1240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(4417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(641,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I40_J_0) ).
thf(3028,plain,
c_Int_OMin != c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(2345,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(907,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(3647,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[907]) ).
thf(1096,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(4080,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1029,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(3931,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(802,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(3408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[802]) ).
thf(828,axiom,
! [A: $i] :
( ( A @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( A @ c_HOL_Ouminus__class_Ouminus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__mult__minus_0) ).
thf(3467,plain,
! [A: $i] :
( ( A @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( A @ c_HOL_Ouminus__class_Ouminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(964,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(3782,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1472,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div_H_6) ).
thf(4957,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL )
| ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(258,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(2157,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(358,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(2377,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)],[358]) ).
thf(500,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_2) ).
thf(2709,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(4525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(467,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__square_0) ).
thf(2631,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(663,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).
thf(3078,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(629,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(3001,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(1412,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_FFT__Mirabelle_Oroot )
= c_Complex_Oii ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root4_0) ).
thf(4817,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_FFT__Mirabelle_Oroot )
= c_Complex_Oii ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(1044,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__cube_0) ).
thf(3968,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).
thf(4123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(2245,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)],[299]) ).
thf(1514,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_HOL_Oone__class_Oone @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(5053,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_HOL_Oone__class_Oone @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(1557,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(5145,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(1762,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(737,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/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).
thf(3254,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)],[737]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(2100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(1772,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)],[95]) ).
thf(1536,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__power__nat_1) ).
thf(5098,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).
thf(3122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[682]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_0) ).
thf(2946,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(581,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(2895,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).
thf(4248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( 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)],[1165]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= C )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(2359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= C )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).
thf(4486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1270]) ).
thf(1081,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
thf(4048,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__even__power_0) ).
thf(1856,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(493,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(2692,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(1587,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)],[10]) ).
thf(415,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(2509,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
thf(3102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[673]) ).
thf(49,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).
thf(1672,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(931,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fact_Ofact__0__nat_0) ).
thf(3704,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(849,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(3518,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1042,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(3963,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1461,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 ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__ge__zero_0) ).
thf(4930,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 ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__one_0) ).
thf(1719,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1157,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(4227,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(900,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/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(3632,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)],[900]) ).
thf(681,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel1_0) ).
thf(3119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(908,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__nat__number__of_1) ).
thf(3650,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1063,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(4012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(1022,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = D )
| ( ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(3916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = D )
| ( ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(730,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(3237,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(2268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(716,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__if_1) ).
thf(3205,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1154,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__one__odd__power_0) ).
thf(4219,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(1202,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 @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).
thf(4333,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 @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1202]) ).
thf(1283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(4518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1283]) ).
thf(1504,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( 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 ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__diff_0) ).
thf(5031,plain,
! [C: $i,B: $i,A: $i] :
( ( ( 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 ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(1310,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(4582,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(553,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
thf(2830,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[553]) ).
thf(935,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__odd__eq_0) ).
thf(3714,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(378,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
thf(2419,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1142,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(4191,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(346,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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).
thf(2349,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)],[346]) ).
thf(1350,axiom,
! [B: $i,A: $i] :
( ( ( 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 ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__square__number__of_0) ).
thf(4676,plain,
! [B: $i,A: $i] :
( ( ( 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 ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(1182,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(4291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(539,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(2798,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(1683,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(690,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(3141,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(573,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).
thf(2877,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[573]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1942,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)],[166]) ).
thf(1024,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(3922,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1483,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
thf(4983,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(993,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(3846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[993]) ).
thf(718,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
thf(3210,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_2) ).
thf(2561,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).
thf(4772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1392]) ).
thf(1371,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).
thf(4721,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)],[1371]) ).
thf(1132,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__div__equality_H_0) ).
thf(4167,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(80,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1739,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1243,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(4425,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)],[1243]) ).
thf(569,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
thf(2868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[569]) ).
thf(885,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(3596,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1194,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_0) ).
thf(4315,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(816,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(3441,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(392,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(2455,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1295,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/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(4545,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)],[1295]) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
thf(2080,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)],[224]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(2053,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[213]) ).
thf(297,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/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(2240,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)],[297]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(1842,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(643,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(3032,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1937,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)],[164]) ).
thf(111,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(1810,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1431,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(4861,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(1338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(4648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1338]) ).
thf(811,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_1) ).
thf(3428,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(2108,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(2038,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(2551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(917,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= C )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(3671,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[917]) ).
thf(939,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(3723,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(905,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fact_Ofact__Suc_0) ).
thf(3643,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(1889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(866,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(3555,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(399,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/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
thf(2472,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)],[399]) ).
thf(1138,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(4180,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[1138]) ).
thf(332,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/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
thf(2317,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)],[332]) ).
thf(753,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).
thf(3294,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(1744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(413,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(2504,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)],[413]) ).
thf(1424,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(4846,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(967,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(3787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1091,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( 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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_2) ).
thf(4068,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( 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)],[1091]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
thf(1668,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1268,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(4482,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(185,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_0) ).
thf(1984,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 @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
thf(2272,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(720,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(3215,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1406,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_5) ).
thf(4804,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(732,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(3242,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(836,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( C @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
thf(3486,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( C @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(910,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(3654,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(2536,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)],[427]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_5) ).
thf(2681,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(406,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
thf(2487,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(454,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div_5) ).
thf(2598,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1478,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(4970,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(948,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I8_J_0) ).
thf(3743,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(4237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(795,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(3390,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(723,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).
thf(3222,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1463,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(4934,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(1293,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(4540,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(859,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(3540,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(440,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
thf(2566,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
thf(1799,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1369,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(4717,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(1159,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__less_0) ).
thf(4231,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(1852,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(546,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_FFT__Mirabelle_Oroot )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root0_0) ).
thf(2813,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_FFT__Mirabelle_Oroot )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(734,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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).
thf(3247,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)],[734]) ).
thf(1117,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/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(4135,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)],[1117]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(2766,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(926,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(3692,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(2482,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(1599,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)],[17]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(2697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(771,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(3333,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(1470,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 ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_power2__le__imp__le_0) ).
thf(4953,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 ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[1470]) ).
thf(657,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(3064,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(4152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[1125]) ).
thf(1169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel_0) ).
thf(4259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(182,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
thf(1979,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(631,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(3005,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)],[631]) ).
thf(251,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(2140,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1098,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 @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power2_1) ).
thf(4086,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 @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[1098]) ).
thf(520,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(2756,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[520]) ).
thf(822,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).
thf(3454,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(832,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(3476,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(953,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(3755,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(984,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(3824,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)],[984]) ).
thf(988,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mod_0) ).
thf(3834,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
thf(2926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[596]) ).
thf(1336,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(4644,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(1266,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus__one_0) ).
thf(4476,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(2402,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)],[370]) ).
thf(1452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(4906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(461,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/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
thf(2617,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)],[461]) ).
thf(1181,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2_0) ).
thf(4288,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(2702,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(432,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( E @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).
thf(2546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( E @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_2) ).
thf(2761,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(897,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(3624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1327,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__div__eq__add3__div__number__of_0) ).
thf(4625,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(1532,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(5090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1532]) ).
thf(1304,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(4567,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(1396,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(4782,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(747,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).
thf(3279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[747]) ).
thf(1443,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_1) ).
thf(4889,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(880,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(3587,plain,
tc_nat @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(3183,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).
thf(1712,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)],[68]) ).
thf(759,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(3306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(2408,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)],[373]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(2089,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(845,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__lemma_0) ).
thf(3508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(1895,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(474,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(2645,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).
thf(1616,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)],[24]) ).
thf(380,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/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
thf(2423,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)],[380]) ).
thf(424,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
thf(2529,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)],[424]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1306,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__m1__odd_0) ).
thf(4572,plain,
! [B: $i,A: $i] :
( ( ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(588,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( E @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).
thf(2909,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( E @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(4550,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(976,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(3807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
thf(1727,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1115,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(4131,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)],[1115]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(1680,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)],[53]) ).
thf(647,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_2) ).
thf(3042,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(738,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).
thf(3257,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1437,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
thf(4874,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(1052,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
thf(3985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1511,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).
thf(5048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1511]) ).
thf(1302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
thf(4562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1302]) ).
thf(751,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(3289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(969,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(3792,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1534,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__special_I2_J_1) ).
thf(5095,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(1509,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(5043,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
thf(2121,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)],[241]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
thf(2235,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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(253,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/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
thf(2144,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)],[253]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(2677,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(2176,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(4685,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[1354]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(1754,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)],[88]) ).
thf(322,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(2292,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
thf(4380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1223]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
thf(2556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1109,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/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(4116,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)],[1109]) ).
thf(782,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult2__eq_0) ).
thf(3358,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(303,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/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(2253,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)],[303]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(2149,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1238,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).
thf(4412,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1238]) ).
thf(1168,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 @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
thf(4256,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 @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1249,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(4438,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(83,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(1747,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(945,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/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(3738,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)],[945]) ).
thf(1205,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
thf(4340,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(1173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
thf(4269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1173]) ).
thf(923,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 @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).
thf(3686,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 @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[923]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(2524,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(797,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(3396,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1256,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/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(4453,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)],[1256]) ).
thf(788,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult1__eq_0) ).
thf(3372,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(1058,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(4000,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(660,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_3) ).
thf(3070,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[660]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(2225,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1273,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).
thf(4494,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(731,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).
thf(3240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[731]) ).
thf(850,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).
thf(3519,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[850]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
thf(1620,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)],[26]) ).
thf(744,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(3272,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(1261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).
thf(4465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1261]) ).
thf(503,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ c_Int_OBit1 @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I9_J_1) ).
thf(2716,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ c_Int_OBit1 @ ( c_Int_OMin @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(176,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 ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(1965,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 ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(494,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 @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).
thf(2695,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 @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[494]) ).
thf(1398,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
thf(4786,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[1398]) ).
thf(1466,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).
thf(4943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1466]) ).
thf(947,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(3741,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(862,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(3547,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(616,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div__lemma_1) ).
thf(2970,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(765,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).
thf(3319,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(958,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(3768,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(1916,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[155]) ).
thf(1026,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).
thf(3925,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1026]) ).
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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
thf(2859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[565]) ).
thf(601,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__1_0) ).
thf(2938,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1520,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( E @ ( C @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I29_J_0) ).
thf(5065,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( E @ ( C @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(1128,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(4159,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(2188,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1191,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(4309,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(365,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
thf(2393,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(667,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
thf(3086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[667]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(1652,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)],[40]) ).
thf(954,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(3758,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1035,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(3945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(749,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(3283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ c_HOL_Oone__class_Oone @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(3266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ c_HOL_Oone__class_Oone @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_0) ).
thf(2674,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(2016,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)],[198]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(2514,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1512,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
thf(5050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1512]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__even__power_H_0) ).
thf(2991,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1535,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(5097,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(824,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).
thf(3458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[824]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(1795,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(2398,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1200,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_1) ).
thf(4328,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1313,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(4590,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(1480,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_0) ).
thf(4975,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(1322,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(4612,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)],[1322]) ).
thf(1391,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).
thf(4769,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(552,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(2827,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(247,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__le__dividend_0) ).
thf(2134,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1277,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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).
thf(4505,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)],[1277]) ).
thf(611,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(2959,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(719,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(3213,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1166,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(4251,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
thf(4978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1481]) ).
thf(287,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).
thf(2220,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)],[287]) ).
thf(652,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_1) ).
thf(3051,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(814,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
= ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I113_J_0) ).
thf(3436,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
= ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(929,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_2) ).
thf(3700,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1175,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__int__code_I13_J_0) ).
thf(4273,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(669,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__self__div__2_0) ).
thf(3091,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(872,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
thf(3568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[872]) ).
thf(702,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(3170,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(855,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/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
thf(3532,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)],[855]) ).
thf(1292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(4537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(971,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(3796,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(639,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 @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__power__less__zero_0) ).
thf(3023,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 @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1507,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(5039,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(1402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).
thf(4796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1402]) ).
thf(579,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(2891,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(1494,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
thf(5011,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
thf(2308,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(4645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(927,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_0) ).
thf(3695,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(513,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
thf(2738,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(717,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).
thf(3208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(1865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
thf(1635,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)],[32]) ).
thf(600,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
thf(2935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(630,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(3002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(774,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(3340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1530,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(5086,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)],[1530]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(1997,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[191]) ).
thf(1558,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( C @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
thf(5148,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( C @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).
thf(1389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(4764,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(965,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(3783,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_1) ).
thf(2055,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)],[214]) ).
thf(987,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__int__code_I13_J_1) ).
thf(3832,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(2166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1334,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
thf(4640,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(904,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__less__0_0) ).
thf(3641,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1442,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(4887,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(1164,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_0) ).
thf(4245,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(1247,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_2) ).
thf(4433,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[1247]) ).
thf(443,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(2573,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(937,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ ( A @ c_HOL_Otimes__class_Otimes @ ( A @ c_HOL_Oplus__class_Oplus @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Ogb__semiring__axioms_H_0) ).
thf(3719,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ ( A @ c_HOL_Otimes__class_Otimes @ ( A @ c_HOL_Oplus__class_Oplus @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(1368,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(4716,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(2311,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)],[330]) ).
thf(420,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
thf(2521,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(428,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(2538,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(696,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_2) ).
thf(3155,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(4,axiom,
tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
thf(1574,plain,
tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(848,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(3515,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(587,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(2906,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(943,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 )
| ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__imp__eq_0) ).
thf(3732,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 )
| ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(675,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(3106,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1187,axiom,
( c_Int_OMin
= ( c_Int_OMin @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_1) ).
thf(4300,plain,
( c_Int_OMin
= ( c_Int_OMin @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(2119,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1522,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(5071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[1522]) ).
thf(401,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(2478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1218,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 ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__special_I3_J_0) ).
thf(4369,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 ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(226,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/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(2084,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)],[226]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
thf(2214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(361,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
thf(2383,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(376,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(2415,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(1538,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_3) ).
thf(5103,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(3038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[645]) ).
thf(470,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ 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__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__special_I1_J_1) ).
thf(2637,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ 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__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1455,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
thf(4914,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(1360,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 @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(4699,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 @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(1722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1119,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(4139,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(2116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(557,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_0) ).
thf(2839,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1151,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult2__eq_0) ).
thf(4213,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(1324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(4616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(1093,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(4073,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1126,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(4154,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(1347,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).
thf(4667,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( 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)],[1347]) ).
thf(1136,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(4176,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(688,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I17_J_0) ).
thf(3138,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(58,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1690,plain,
tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(658,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).
thf(3066,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(3,negated_conjecture,
( ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( c_Suc @ c_COMBB ) ) ) ) @ ( v_a____ @ c_COMBB ) ) ) ) @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_OIDFT ) ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( v_a____ @ c_COMBB ) ) ) ) @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_OIDFT ) ) @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( c_Suc @ c_COMBB ) ) ) ) @ ( v_a____ @ c_COMBB ) ) ) ) @ ( v_ka____ @ c_FFT__Mirabelle_OIFFT ) @ hAPP ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( v_a____ @ c_COMBB ) ) ) ) @ ( v_ka____ @ c_FFT__Mirabelle_OIFFT ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(1571,plain,
( ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( c_Suc @ c_COMBB ) ) ) ) @ ( v_a____ @ c_COMBB ) ) ) ) @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_OIDFT ) ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( v_a____ @ c_COMBB ) ) ) ) @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_OIDFT ) ) @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( c_Suc @ c_COMBB ) ) ) ) @ ( v_a____ @ c_COMBB ) ) ) ) @ ( v_ka____ @ c_FFT__Mirabelle_OIFFT ) @ hAPP ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( v_ka____ @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_i____ @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( v_a____ @ c_COMBB ) ) ) ) @ ( v_ka____ @ c_FFT__Mirabelle_OIFFT ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(4509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1106,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(4107,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(1969,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(698,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ ( c_Suc @ hAPP ) @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(3160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ ( c_Suc @ hAPP ) @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(2065,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)],[218]) ).
thf(1226,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(4388,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(823,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__int__code_I15_J_1) ).
thf(3456,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(515,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(2742,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).
thf(4420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1241]) ).
thf(1527,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(5082,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(1071,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs__number__of_0) ).
thf(4028,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1426,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).
thf(4850,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1426]) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(2289,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)],[320]) ).
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 @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).
thf(2278,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)],[316]) ).
thf(597,axiom,
( c_Int_OPls
= ( c_Int_OPls @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_1) ).
thf(2928,plain,
( c_Int_OPls
= ( c_Int_OPls @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(618,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(2974,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[618]) ).
thf(1299,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nat__number__of_0) ).
thf(4554,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(551,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(2824,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[551]) ).
thf(1147,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(4203,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1332,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( B @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).
thf(4635,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( B @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(1544,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/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(5114,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)],[1544]) ).
thf(1232,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(4401,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(1245,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(4430,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(1877,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)],[138]) ).
thf(950,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(3747,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(202,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(2025,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(468,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__Suc_0) ).
thf(2632,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(1440,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 ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_power2__less__imp__less_0) ).
thf(4882,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 ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[1440]) ).
thf(654,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__sum_0) ).
thf(3055,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1104,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).
thf(4103,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1104]) ).
thf(331,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/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(2314,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)],[331]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(2343,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)],[343]) ).
thf(464,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(2625,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1419,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
thf(4833,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(1260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(4462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(1454,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(4911,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(2111,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(661,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__2__eq__Suc_0) ).
thf(3073,plain,
! [A: $i] :
( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1089,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(4064,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1089]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(1630,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
thf(2261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(76,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
thf(1731,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(874,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ 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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_1) ).
thf(3572,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ 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)],[874]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).
thf(1909,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)],[152]) ).
thf(1447,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
thf(4897,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(1484,axiom,
! [A: $i] :
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__2__eq__Suc_H_0) ).
thf(4985,plain,
! [A: $i] :
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(2446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1177,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__Suc__mult__two__diff__two_0) ).
thf(4277,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(700,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__0_0) ).
thf(3165,plain,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1149,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_0) ).
thf(4208,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1049,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(3977,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(122,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( 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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1838,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( 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)],[122]) ).
thf(893,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(3614,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(755,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(3298,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(1340,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(4652,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(835,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_1) ).
thf(3483,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1046,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
thf(3971,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(1373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(4726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(482,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(2664,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1000,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
thf(3861,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(694,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__odd__power_0) ).
thf(3150,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).
thf(2842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[558]) ).
thf(1486,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(4990,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(445,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(2578,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(1688,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)],[57]) ).
thf(834,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( F @ ( E @ ( C @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
thf(3480,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( F @ ( E @ ( C @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1516,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( E @ ( G @ ( F @ ( B @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
thf(5057,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( E @ ( G @ ( F @ ( B @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(990,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(3838,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(250,axiom,
tc_Int_Oint @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(2139,plain,
tc_Int_Oint @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(4827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(96,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(1775,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[96]) ).
thf(761,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__0__number__of_0) ).
thf(3310,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(220,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(2069,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)],[220]) ).
thf(527,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_3) ).
thf(2770,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(377,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(2418,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(1423,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(4844,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1423]) ).
thf(1418,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(4832,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(507,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__div__two__times__two__plus__one_0) ).
thf(2725,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
thf(1594,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)],[13]) ).
thf(62,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
thf(1699,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(898,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).
thf(3627,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(2171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(2051,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(524,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(2765,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(809,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__one__even__power_0) ).
thf(3423,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(402,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
thf(2481,plain,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(677,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(3110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(2086,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)],[227]) ).
thf(1276,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I35_J_0) ).
thf(4502,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(1220,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/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(4373,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)],[1220]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
thf(2369,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(918,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(3674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[918]) ).
thf(1038,axiom,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(3953,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(636,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( E @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( C @ ( A @ ( E @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divides__special_0) ).
thf(3016,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( E @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( C @ ( A @ ( E @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(932,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(3706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(767,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(3325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).
thf(4703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1362]) ).
thf(1189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
thf(4304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1189]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(2967,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(364,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/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(2390,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)],[364]) ).
thf(1144,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(4196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(2303,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(847,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/sandbox2/benchmark/theBenchmark.p',cls_number__of__Pls_0) ).
thf(3512,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)],[847]) ).
thf(1274,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(4497,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(1179,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(4282,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(2207,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)],[282]) ).
thf(1555,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(5139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(1019,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/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(3908,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)],[1019]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).
thf(1694,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)],[60]) ).
thf(1476,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(4965,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(622,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
thf(2984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[622]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(1973,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(1805,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(2506,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(1265,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_1) ).
thf(4473,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(633,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__nat__number__of_2) ).
thf(3009,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(168,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(1948,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(711,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).
thf(3193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1316,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(4598,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(1377,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__abs_0) ).
thf(4735,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(692,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( E @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).
thf(3146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( E @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(390,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(2449,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)],[390]) ).
thf(746,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(3278,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(1211,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
thf(4355,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(583,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(2899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(1491,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(5003,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_2) ).
thf(2582,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
thf(2005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1008,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_1) ).
thf(3881,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(817,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(3444,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(1379,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(4741,plain,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(1234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(4405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(1356,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(4690,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(590,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(2914,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ 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)],[590]) ).
thf(642,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(3031,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(548,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I37_J_0) ).
thf(2816,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(1583,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)],[8]) ).
thf(44,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(1662,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[44]) ).
thf(1229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(4394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1031,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ( ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).
thf(3936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ( ( 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)],[1031]) ).
thf(1449,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
thf(4901,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1449]) ).
thf(1258,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(4458,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(2665,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(1434,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(4868,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1434]) ).
thf(1410,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(4813,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(1309,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(4580,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(533,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
thf(2784,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).
thf(4456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1257]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1196,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
thf(4319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1137,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
thf(4177,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(1048,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__int__code_I16_J_1) ).
thf(3975,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
thf(1990,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)],[187]) ).
thf(651,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(3048,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1430,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(4859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).
thf(2684,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(2202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(2333,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)],[338]) ).
thf(1108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_0) ).
thf(4113,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(84,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
thf(1748,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(790,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(3376,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(16,axiom,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).
thf(1598,plain,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(4360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(1021,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__mult__left_0) ).
thf(3913,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1017,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I14_J_0) ).
thf(3904,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1524,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(5074,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(685,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mod_1) ).
thf(3129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(2518,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1526,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).
thf(5079,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(575,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(2882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[575]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
thf(2689,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1079,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(4045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1343,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(4658,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
thf(2942,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1053,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(3988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[1053]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(1845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(106,axiom,
tc_Int_Oint @ class_Ring__and__Field_Olordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).
thf(1798,plain,
tc_Int_Oint @ class_Ring__and__Field_Olordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(2298,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)],[325]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_2) ).
thf(2661,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1549,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(5125,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(1464,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__minus_0) ).
thf(4937,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( 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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(2977,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( 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)],[619]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__le__mono2_0) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(357,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(2375,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)],[357]) ).
thf(1542,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__special_I4_J_0) ).
thf(5111,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(665,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_2) ).
thf(3082,plain,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(276,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(2192,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)],[276]) ).
thf(1349,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(4673,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(19,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1605,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(450,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus1__even_0) ).
thf(2588,plain,
! [B: $i,A: $i] :
( ( ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(1469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(4950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(1458,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).
thf(4922,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(1647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1567,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__plus__one__div__two_0) ).
thf(5171,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(1291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(4534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(912,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(3659,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( 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__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__number__of_1) ).
thf(4469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( 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__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(98,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1780,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)],[98]) ).
thf(87,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
thf(1753,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_0) ).
thf(4961,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(655,axiom,
! [B: $i,A: $i] :
( ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nat__number__of_1) ).
thf(3058,plain,
! [B: $i,A: $i] :
( ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
thf(2386,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(2720,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1004,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(3872,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(1222,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(4377,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(890,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
thf(3608,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[890]) ).
thf(561,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).
thf(2850,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 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[561]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(2160,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)],[260]) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(2569,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)],[441]) ).
thf(819,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__int__code_I15_J_0) ).
thf(3448,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(4346,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1059,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(4003,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(1785,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)],[100]) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(2429,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)],[382]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(2322,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)],[334]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(2044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1518,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(5062,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(348,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/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(2354,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)],[348]) ).
thf(67,axiom,
tc_Int_Oint @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
thf(1711,plain,
tc_Int_Oint @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(637,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(3019,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(664,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/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
thf(3080,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)],[664]) ).
thf(229,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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(2092,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)],[229]) ).
thf(1100,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I17_J_1) ).
thf(4092,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).
thf(1987,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)],[186]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(1716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1033,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(3940,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(758,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(3305,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(262,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
thf(2165,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(981,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(3818,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
thf(1813,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(1637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(679,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(3114,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1496,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( C @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
thf(5015,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( C @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(1067,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_5) ).
thf(4020,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[1067]) ).
thf(1155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).
thf(4222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1155]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
thf(1869,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1122,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/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero_0) ).
thf(4145,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)],[1122]) ).
thf(340,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 @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(2337,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 @ ( C @ ( D @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(314,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
thf(2276,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(973,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I45_J_0) ).
thf(3801,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1980,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)],[183]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
thf(2128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(5154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1560]) ).
thf(960,axiom,
( ( c_Complex_Oii @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_i__mult__eq2_0) ).
thf(3774,plain,
( ( c_Complex_Oii @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(684,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OMin @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OMin @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I13_J_1) ).
thf(3127,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OMin @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OMin @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
thf(4351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1209]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(1901,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(405,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
thf(2486,plain,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_0) ).
thf(2903,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1404,axiom,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).
thf(4800,plain,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(804,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__one__even__power_0) ).
thf(3412,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(870,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__Pls_0) ).
thf(3564,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(996,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
thf(3853,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
thf(5106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1539]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(2247,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(374,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
thf(2411,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1473,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(4959,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
thf(1802,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1271,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(4488,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(2579,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)],[446]) ).
thf(794,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(3388,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(1239,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(4414,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1153,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/sandbox2/benchmark/theBenchmark.p',cls_half_0) ).
thf(4217,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)],[1153]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(1934,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(606,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(2948,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(928,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__power__if_0) ).
thf(3697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(1405,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(4802,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)],[1405]) ).
thf(676,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1__right_0) ).
thf(3107,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1086,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(4057,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(1898,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(909,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).
thf(3652,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus1__odd_0) ).
thf(2558,plain,
! [B: $i,A: $i] :
( ( ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(805,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).
thf(3415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(986,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
thf(3829,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(683,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__eq__diff__pred_0) ).
thf(3124,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(2426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1116,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(4133,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(1702,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[63]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(2379,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1248,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(4436,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(781,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
thf(3356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[781]) ).
thf(1382,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).
thf(4748,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(349,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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(2357,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)],[349]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(2320,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)],[333]) ).
thf(501,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(2711,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(1487,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( B @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
thf(4991,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( B @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(85,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
thf(1749,plain,
tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1121,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I12_J_0) ).
thf(4143,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
thf(4932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1462]) ).
thf(724,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
thf(3224,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(416,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/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
thf(2511,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)],[416]) ).
thf(1331,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__mult__two__ex_1) ).
thf(4634,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(1358,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(4695,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1670,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)],[48]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(2949,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).
thf(2722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(508,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).
thf(2728,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1172,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(4267,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(204,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(2030,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1421,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(4838,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1528,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__ge__Suc__0__nat_0) ).
thf(5083,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(543,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(2807,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(1537,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(5100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(632,axiom,
~ ( tc_Int_Oint @ ( c_Int_OPls @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I2_J_0) ).
thf(3007,plain,
~ ( tc_Int_Oint @ ( c_Int_OPls @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(2266,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)],[309]) ).
thf(1282,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(4516,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(1124,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
thf(4150,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1124]) ).
thf(448,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).
thf(2584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[448]) ).
thf(798,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).
thf(3398,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[798]) ).
thf(1413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(4819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1413]) ).
thf(922,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/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(3684,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)],[922]) ).
thf(1228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(4392,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(2875,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(813,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(3433,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(879,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(3584,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(821,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__2__eq__2_0) ).
thf(3452,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(799,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(3401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1467,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).
thf(4945,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1467]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
thf(1685,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(1817,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[114]) ).
thf(1005,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( B @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(3874,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( B @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1005]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(2347,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(2209,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
thf(2643,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[473]) ).
thf(1375,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= F )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(4730,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= F )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(884,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(3593,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(2013,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(595,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).
thf(2924,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[595]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__int__code_I16_J_0) ).
thf(2626,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit1 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(156,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
thf(1918,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(347,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(2352,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[347]) ).
thf(882,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
thf(3589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[882]) ).
thf(1199,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__power__if_1) ).
thf(4325,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(570,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(2870,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(4165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1436,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(4873,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(1342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).
thf(4656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1342]) ).
thf(1489,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( C @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
thf(4997,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( C @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(709,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(3188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1378,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).
thf(4738,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(1395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
thf(4780,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(2325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(1140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(4185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ( tc_Int_Oint @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = A )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zless__linear_0) ).
thf(2919,plain,
! [B: $i,A: $i] :
( ( tc_Int_Oint @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = A )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
thf(1575,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)],[5]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus1__divide_0) ).
thf(2071,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( 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)],[221]) ).
thf(480,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(2658,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(2775,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[529]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1734,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[78]) ).
thf(1521,axiom,
! [A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__power2_0) ).
thf(5068,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(536,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
thf(2792,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
thf(1807,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1088,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(4061,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(499,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/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero__iff_0) ).
thf(2707,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)],[499]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(2098,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)],[231]) ).
thf(302,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(2251,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)],[302]) ).
thf(1552,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/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__1_0) ).
thf(5132,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)],[1552]) ).
thf(1353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
thf(4683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1353]) ).
thf(772,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__eq_0) ).
thf(3336,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).
thf(2431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(736,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(3252,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 @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(366,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(2394,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)],[366]) ).
thf(827,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).
thf(3465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(2591,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)],[451]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(1590,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1515,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(5055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(1111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).
thf(4121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(1020,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
thf(3911,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(1365,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(4710,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(624,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ( 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/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(2988,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ( 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)],[624]) ).
thf(1001,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).
thf(3864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1001]) ).
thf(452,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(2594,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
thf(2174,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(2283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(968,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(3789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).
thf(2855,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[563]) ).
thf(933,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( B @ 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__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__special_I3_J_1) ).
thf(3709,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( B @ 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__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1639,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)],[34]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(1903,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(248,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(2135,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)],[248]) ).
thf(1493,axiom,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
thf(5008,plain,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).
thf(1099,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
thf(4089,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(435,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(2554,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1113,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).
thf(4126,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1113]) ).
thf(722,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(3220,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1077,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(4042,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(545,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(2811,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(1400,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/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(4791,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)],[1400]) ).
thf(674,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).
thf(3104,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[674]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(1854,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)],[128]) ).
thf(1204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(4338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(842,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(3501,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)],[842]) ).
thf(116,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(1822,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1062,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(4010,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(1363,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mod__eq__add3__mod_0) ).
thf(4705,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(245,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
thf(2130,plain,
tc_Int_Oint @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(999,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(3859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(769,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(3331,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(786,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__Suc__Suc_0) ).
thf(3368,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(913,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(3662,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)],[913]) ).
thf(963,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(3780,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1448,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(4900,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
thf(2152,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)],[256]) ).
thf(604,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(2944,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).
thf(2956,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[610]) ).
thf(1387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).
thf(4759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1387]) ).
thf(351,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(2362,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)],[351]) ).
thf(488,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(2680,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(1546,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(5119,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(955,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).
thf(3761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[955]) ).
thf(808,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).
thf(3420,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1139,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/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
thf(4182,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)],[1139]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(1861,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)],[131]) ).
thf(400,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/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(2475,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)],[400]) ).
thf(1428,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(4855,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(1318,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(4602,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__0__le__power__imp__0__le_0) ).
thf(2796,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1564,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(5164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(1563,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__pos_0) ).
thf(5162,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(1183,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__0__number__of_1) ).
thf(4293,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(589,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
thf(2912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[589]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(2041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(840,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(3497,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1007,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(3879,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[1007]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(2648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(812,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
= ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(3430,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
= ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
thf(1777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(395,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(2462,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)],[395]) ).
thf(1393,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(4774,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(1186,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(4299,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1500,axiom,
tc_nat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(5023,plain,
tc_nat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(2330,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1014,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(3896,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1014]) ).
thf(278,axiom,
tc_Int_Oint @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(2198,plain,
tc_Int_Oint @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(854,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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(3529,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)],[854]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1706,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)],[65]) ).
thf(779,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(3351,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1055,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).
thf(3993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1055]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
thf(2095,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1253,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(4446,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(292,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(2230,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(2294,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[323]) ).
thf(906,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div__lemma_2) ).
thf(3645,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
thf(2494,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)],[409]) ).
thf(1305,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OMin @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OMin @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I13_J_0) ).
thf(4570,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OMin @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OMin @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(189,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
thf(1994,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1190,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).
thf(4306,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(864,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(3552,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1460,axiom,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Min_0) ).
thf(4927,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(2779,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1325,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(4619,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(1401,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq__number__of_2) ).
thf(4794,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(1725,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)],[73]) ).
thf(752,axiom,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__not__one_0) ).
thf(3291,plain,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1409,axiom,
! [A: $i] :
( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(4811,plain,
! [A: $i] :
( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
thf(2233,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(1012,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(3892,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(1625,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)],[28]) ).
thf(421,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/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
thf(2522,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)],[421]) ).
thf(12,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).
thf(1593,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(851,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(3521,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(1673,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)],[50]) ).
thf(686,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( 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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(3132,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( 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)],[686]) ).
thf(1217,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).
thf(4367,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(715,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(3203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(151,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
thf(1908,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
thf(2142,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(791,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
thf(3379,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(598,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
thf(2930,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(305,axiom,
tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
thf(2258,plain,
tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(356,axiom,
tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
thf(2374,plain,
tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1439,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc3__eq__add__3_0) ).
thf(4880,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(1076,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(4039,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
thf(1642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1456,axiom,
! [C: $i,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 ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_1) ).
thf(4917,plain,
! [C: $i,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 ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[1456]) ).
thf(1064,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(4014,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
thf(1957,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1551,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__diff__Suc_0) ).
thf(5129,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(1231,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(4399,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(1355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(4687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(1348,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(4670,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(966,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__special_I1_J_0) ).
thf(3785,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(257,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(2155,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(426,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/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
thf(2534,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)],[426]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(2255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(1408,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_1) ).
thf(4809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(621,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
thf(2983,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(608,axiom,
! [A: $i] :
~ ( tc_Int_Oint @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zless__le_1) ).
thf(2951,plain,
! [A: $i] :
~ ( tc_Int_Oint @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_1) ).
thf(4523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(547,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(2815,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(2008,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1422,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
thf(4841,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(1212,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(4357,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(1272,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_0) ).
thf(4491,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(1757,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(925,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(3690,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 @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1495,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_Suc @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__Suc_0) ).
thf(5014,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_Suc @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
thf(2768,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(829,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( E @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).
thf(3469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( E @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1508,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(5041,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)],[1508]) ).
thf(768,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(3328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1083,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__power__less__imp__less_0) ).
thf(4051,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(1562,axiom,
! [A: $i] :
( ( c_Int_OMin = A )
| ( c_Int_OMin
!= ( A @ c_Int_OBit1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_0) ).
thf(5159,plain,
! [A: $i] :
( ( c_Int_OMin = A )
| ( c_Int_OMin
!= ( A @ c_Int_OBit1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(1150,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I36_J_0) ).
thf(4210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(1244,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(4427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
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_lessequals ) ) )
| ( ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
thf(1789,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(353,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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).
thf(2366,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)],[353]) ).
thf(612,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(2961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(371,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
thf(2404,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(289,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/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
thf(2223,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)],[289]) ).
thf(462,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
thf(2619,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( C @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(484,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).
thf(2668,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_nat @ ( E @ ( B @ ( D @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( E @ ( C @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(1742,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1051,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__power__le__0__imp__0_0) ).
thf(3982,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(983,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
thf(3822,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[983]) ).
thf(518,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( E @ ( G @ ( F @ ( C @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
thf(2751,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( E @ ( G @ ( F @ ( C @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(2800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1039,axiom,
! [A: $i] :
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2__right_0) ).
thf(3956,plain,
! [A: $i] :
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(1385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__power2__lt__zero_0) ).
thf(4755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(1657,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)],[42]) ).
thf(1533,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(5092,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(1446,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__power__nat_2) ).
thf(4895,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(272,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(2186,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(777,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(3347,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(4631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(705,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(3177,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(974,axiom,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(3804,plain,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1477,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__odd__power_1) ).
thf(4968,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(517,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).
thf(2746,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1127,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(4157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1498,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(5019,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(1097,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).
thf(4083,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1069,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(4024,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(995,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_1) ).
thf(3850,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(498,axiom,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I42_J_0) ).
thf(2704,plain,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(502,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).
thf(2714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[502]) ).
thf(810,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I10_J_0) ).
thf(3426,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( c_Int_OPls @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(1251,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__gt__zero__nat_0) ).
thf(4442,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1074,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(4034,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(649,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(3045,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(844,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(3506,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(992,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).
thf(3843,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).
thf(2021,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)],[200]) ).
thf(217,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(2063,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[217]) ).
thf(1541,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(5110,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(975,axiom,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I4_J_0) ).
thf(3805,plain,
! [A: $i] :
( ~ ( tc_Int_Oint @ ( A @ c_Int_OBit0 @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( A @ ( c_Int_OPls @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(477,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(2651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[477]) ).
thf(733,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div_1) ).
thf(3244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( A @ ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(412,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(2502,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 @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(119,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 ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
thf(1829,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 ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(860,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__Suc__0_0) ).
thf(3543,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1559,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/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I110_J_0) ).
thf(5151,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)],[1559]) ).
thf(783,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(3360,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(1003,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/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
thf(3869,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)],[1003]) ).
thf(837,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).
thf(3489,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(4239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(1158,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( E @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).
thf(4229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( E @ ( D @ ( B @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( E @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1471,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__Suc_0) ).
thf(4955,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(1215,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(4363,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(784,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(3362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[784]) ).
thf(509,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(2731,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[509]) ).
thf(640,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(3025,plain,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
thf(1827,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)],[118]) ).
thf(541,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(2803,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1163,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/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).
thf(4242,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)],[1163]) ).
thf(560,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
thf(2847,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).
thf(2600,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[455]) ).
thf(1224,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(4382,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(873,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/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
thf(3570,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)],[873]) ).
thf(889,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I37_J_0) ).
thf(3605,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1479,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ( ( tc_nat @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff_0) ).
thf(4972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ( ( tc_nat @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(181,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
thf(1976,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 @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1485,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
thf(4987,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).
thf(739,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 @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(3259,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 @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(1090,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).
thf(4066,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 @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1090]) ).
thf(1043,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( c_Suc @ hAPP ) )
= B )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(3965,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( c_Suc @ hAPP ) )
= B )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(1923,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1517,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).
thf(5060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[1517]) ).
thf(1510,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
thf(5046,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(1148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).
thf(4206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(858,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div_0) ).
thf(3538,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1925,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)],[160]) ).
thf(1201,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(4330,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(1032,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(3939,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(429,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 @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).
thf(2539,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 @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[429]) ).
thf(15,axiom,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
thf(1597,plain,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I14_J_1) ).
thf(2864,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit0 @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(946,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(3740,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(1092,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(4071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[1092]) ).
thf(678,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(3113,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(2484,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[404]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(1885,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(2699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(978,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).
thf(3812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[978]) ).
thf(1174,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(4271,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 @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(2270,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[311]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(1606,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)],[20]) ).
thf(574,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( C @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( c_Suc @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I27_J_0) ).
thf(2879,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( C @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( c_Suc @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(1444,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(4891,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(2998,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[628]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(1848,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[125]) ).
thf(1432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(4863,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(754,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(3296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[754]) ).
thf(916,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__mod__add3_0) ).
thf(3669,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1016,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(3901,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(635,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).
thf(3013,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[635]) ).
thf(853,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
thf(3526,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1041,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1_0) ).
thf(3960,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(519,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(2754,plain,
! [B: $i,A: $i] :
( ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1203,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).
thf(4335,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(1037,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(3950,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1503,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I115_J_0) ).
thf(5029,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(1523,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(5073,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(1284,axiom,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(4520,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(1335,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(4642,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(725,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__3__eq__3_0) ).
thf(3227,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1328,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(4627,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(1962,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(439,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(2563,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)],[439]) ).
thf(1025,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(3924,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(1945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1372,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).
thf(4723,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_1) ).
thf(3096,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1397,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(4784,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(577,axiom,
( ( tc_nat @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__Min_0) ).
thf(2887,plain,
( ( tc_nat @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1390,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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).
thf(4767,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)],[1390]) ).
thf(801,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__one__odd__power_0) ).
thf(3405,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(222,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(2074,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(2018,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)],[199]) ).
thf(568,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I16_J_0) ).
thf(2866,plain,
! [B: $i,A: $i] :
( ~ ( tc_Int_Oint @ ( B @ c_Int_OBit0 @ ( A @ c_Int_OBit1 @ c_HOL_Oord__class_Oless ) ) )
| ( tc_Int_Oint @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(554,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(2832,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1296,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
thf(4547,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(385,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/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(2436,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)],[385]) ).
thf(386,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/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(2438,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)],[386]) ).
thf(1193,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__div__eq__add3__div_0) ).
thf(4313,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(460,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
thf(2615,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 @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[460]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(764,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(3316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(555,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(2834,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(626,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
thf(2993,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(714,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_4) ).
thf(3200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(275,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
thf(2191,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(235,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
thf(2106,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)],[235]) ).
thf(1030,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(3933,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)],[1030]) ).
thf(865,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_2) ).
thf(3553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(938,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(3721,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
thf(4174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ 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)],[1135]) ).
thf(1465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(4940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(620,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
thf(2980,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(644,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_0) ).
thf(3035,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( A @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(875,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/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(3575,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)],[875]) ).
thf(1298,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div2__Suc__Suc_0) ).
thf(4552,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Suc @ hAPP ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(479,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/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(2655,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)],[479]) ).
thf(13048,plain,
$false,
inference(e,[status(thm)],[2163,5116,1633,3167,2412,2544,3927,4682,4877,1950,2250,2199,3021,2822,4188,1586,4201,2452,4560,1879,2612,4094,5088,2744,2889,2306,3053,4450,3345,4005,2341,4824,2131,4909,4262,1767,1995,3930,4169,4022,1729,3477,3979,3581,4852,2787,1850,2499,3969,1982,3566,4728,2280,4904,3172,2077,3990,1882,2622,4311,2381,1618,2953,2671,4711,4215,4408,4592,1750,3185,4714,4037,2940,1596,5000,3417,2527,3040,4391,3460,1569,4807,1939,4697,2114,2837,1971,1793,4614,3382,4479,4532,4105,1655,3745,2686,4575,3044,2933,3616,4564,2901,2575,3848,2195,4543,5120,3217,4234,5037,1608,4403,2035,3332,3942,3135,4097,4884,3365,4870,2740,2918,4110,4528,2184,3175,1999,3446,4638,1872,4856,4440,4650,2168,1919,2459,5005,3562,1954,2844,2146,4980,3895,3717,3370,4047,1835,3545,4679,3088,1613,3308,3281,2082,4607,2516,4610,3597,3836,4343,3236,3629,2972,3634,3766,1914,2491,2763,2548,1782,2227,5123,3249,4371,4079,1650,3730,1645,1921,3140,4137,2400,4963,4322,2819,4948,2531,4467,2405,3688,4775,4511,5024,1628,3263,3275,3116,3342,3495,4224,3821,5064,2274,3776,3855,2571,2603,2916,3195,4743,4866,1792,2735,4422,1760,1660,3046,2339,4692,4761,3061,4654,2444,2217,3612,3148,4275,4349,3410,1577,3749,2488,1832,2897,1992,3353,2466,5108,2126,2420,3099,1704,4664,4141,2158,4265,5076,4595,4119,3998,3840,1892,3463,3374,3385,2857,4353,4788,2169,3638,4194,4358,2049,5127,4622,3919,4830,4317,3084,2635,5052,3312,3657,1931,2024,1641,2301,1815,4460,3180,4471,4507,3557,1875,5020,3602,2852,3231,2388,3866,4302,4514,4253,4008,2237,3322,3524,4847,4815,5156,2291,1677,2335,4432,2456,2222,4411,1664,2794,3887,1714,2027,4903,3075,4443,5084,4578,2105,4018,5027,3393,2996,3724,1911,4600,2782,2893,4297,2469,4733,2259,3163,2650,3473,3702,1858,3438,4147,4050,3621,3973,1960,3093,5135,4798,2777,3152,3771,4162,2964,2058,4033,2861,2190,4701,2103,4718,4751,4660,3537,1928,4055,3068,4364,1622,2371,2772,3157,3676,2137,4924,5169,2002,2809,2242,2286,2639,5137,4707,3588,3559,4285,3906,4588,3492,2718,2205,1696,2586,2884,4483,3510,1863,3857,1691,5167,5034,1708,2641,3679,3899,2922,5174,2011,3582,3229,3011,4604,3450,3503,4199,4893,4323,3591,3301,3303,4753,4407,4629,4531,5017,3635,2364,5142,4557,3995,2047,4076,2737,2232,2296,4031,1736,4100,2496,2790,4059,2905,1868,2061,3550,4172,3418,3795,2441,3735,2264,3261,3827,2541,4375,1666,3610,2969,4449,4836,3711,2733,4016,2805,2596,4397,4920,1580,2277,1570,1676,3752,4521,4128,3233,3884,4499,2606,1824,3816,2032,4821,3814,2986,4160,4661,3664,2396,3682,3339,3778,3889,3471,4044,3286,1883,3948,3314,3578,2609,2179,2327,2211,3763,3727,3667,3799,4027,2653,3958,4295,3191,2464,4280,2758,2873,3269,1602,3618,2628,3810,4053,4585,2433,3403,1968,3198,4994,4757,3499,3349,4385,1951,1888,3877,3600,1687,2068,1819,3144,4746,3535,1787,5113,2181,4417,3028,2345,3647,4080,3931,3408,3467,3782,4957,2157,2377,2709,4525,2631,3078,3001,4817,3968,4123,2245,5053,5145,1762,3254,2100,1772,5098,3122,2946,2895,4248,2359,4486,4048,1856,2692,1587,2509,3102,1672,3704,3518,3963,4930,1719,4227,3632,3119,3650,4012,3916,3237,2268,3205,4219,4333,4518,5031,4582,2830,3714,2419,4191,2349,4676,4291,2798,1683,3141,2877,1942,3922,4983,3846,3210,2561,4772,4721,4167,1739,4425,2868,3596,4315,3441,2455,4545,2080,2053,2240,1842,3032,1937,1810,4861,4648,3428,2108,2038,2551,3671,3723,3643,1889,3555,2472,4180,2317,3294,1744,2504,4846,3787,4068,1668,4482,1984,2272,3215,4804,3242,3486,3654,2536,2681,2487,2598,4970,3743,4237,3390,3222,4934,4540,3540,2566,1799,4717,4231,1852,2813,3247,4135,2766,3692,2482,1599,2697,3333,4953,3064,4152,4259,1979,3005,2140,4086,2756,3454,3476,3755,3824,3834,2926,4644,4476,2402,4906,2617,4288,2702,2546,2761,3624,4625,5090,4567,4782,3279,4889,3587,3183,1712,3306,2408,2089,3508,1895,2645,1616,2423,2529,1732,4572,2909,4550,3807,1906,1727,4131,1680,3042,3257,4874,3985,5048,4562,3289,3792,5095,5043,2121,2235,2144,2677,2176,4685,1754,2292,4380,2556,4116,3358,2253,2149,4412,4256,4438,1747,3738,4340,4269,3686,2524,3396,4453,3372,4000,3070,2225,4494,3240,3519,1620,3272,4465,2716,1965,2695,4786,4943,3741,3547,2970,3319,3768,1916,3925,2859,2938,5065,4159,2188,4309,2393,3086,1652,3758,3945,3283,3266,2674,2016,2514,5050,2991,5097,3458,1795,2398,4328,4590,4975,4612,4769,2827,2134,4505,2959,3213,4251,4978,2220,3051,3436,3700,4273,3091,3568,3170,3532,4537,3796,3023,5039,4796,2891,5011,2308,4645,3695,2738,3208,1865,1635,2935,3002,3340,5086,1997,5148,4764,3783,2055,3832,2166,1765,4640,3641,4887,4245,4433,2573,3719,4716,2311,2521,2538,3155,1574,3515,2906,3732,3106,4300,2119,5071,2478,4369,2084,2214,2383,2415,5103,3038,2637,4914,4699,1722,4139,2116,2839,4213,4616,4073,4154,4667,4176,3138,1690,3066,1571,4509,4107,1969,3160,2065,4388,3456,2742,4420,5082,4028,4850,2289,2278,2928,2974,4554,2824,4203,4635,5114,4401,4430,1877,3747,2025,2632,4882,3055,4103,2314,2343,2625,4833,4462,4911,2111,3073,4064,1630,2261,1731,3572,1909,4897,4985,2446,4277,3165,4208,3977,1838,3614,3298,4652,3483,3971,4726,2664,3861,3150,2842,4990,2578,1688,3480,5057,3838,2139,4827,1775,3310,2069,2770,2418,4844,4832,2725,1594,1699,3627,2171,2051,2765,3423,2481,3110,2086,4502,4373,2369,3674,3953,3016,3706,3325,4703,4304,2967,2390,4196,2303,3512,4497,4282,2207,5139,3908,1694,4965,2984,1973,1805,2506,4473,3009,1948,3193,4598,4735,3146,2449,3278,4355,2899,5003,2582,2005,3881,3444,4741,4405,4690,2914,3031,2816,1583,1662,4394,3936,4901,4458,2665,4868,4813,4580,2784,4456,2124,4319,4177,3975,1990,3048,4859,2684,2202,2333,4113,1748,3376,1598,4360,3913,3904,5074,3129,2518,5079,2882,2689,4045,4658,2942,3988,1845,1798,2298,2661,5125,4937,2977,1611,2375,5111,3082,2192,4673,1605,2588,4950,4922,1647,5171,4534,3659,4469,1780,1753,4961,3058,2386,2720,3872,4377,3608,2850,2160,2569,3448,4346,4003,1785,2429,2322,2044,5062,2354,1711,3019,3080,2092,4092,1987,1716,3940,3305,2165,3818,1813,1637,3114,5015,4020,4222,1869,4145,2337,2276,3801,1980,2128,5154,3774,3127,4351,1901,2486,2903,4800,3412,3564,3853,5106,2247,2411,4959,1802,4488,2579,3388,4414,4217,1934,2948,3697,4802,3107,4057,1898,3652,2558,3415,3829,3124,2426,4133,1702,2379,4436,3356,4748,2357,1955,2320,2711,4991,1749,4143,4932,3224,2511,4634,4695,1670,2949,2722,2728,4267,2030,4838,5083,2807,5100,3007,2266,4516,4150,2584,3398,4819,3684,4392,2875,3433,3584,3452,3401,4945,1685,1817,3874,2347,2209,2643,4730,3593,2013,2924,2626,1918,2352,3589,4325,2870,4165,4873,4656,4997,3188,4738,4780,2325,4185,2919,1575,2071,2658,2775,1734,5068,2792,1807,4061,2707,2098,2251,5132,4683,3336,2431,3252,2394,3465,2591,1590,5055,4121,3911,4710,2988,3864,2594,2174,2283,3789,2855,3709,1639,1903,2135,5008,4089,2554,4126,3220,4042,2811,4791,3104,1854,4338,3501,1822,4010,4705,2130,3859,3331,3368,3662,3780,4900,2152,2944,2956,4759,2362,2680,5119,3761,3420,4182,1861,2475,4855,4602,2796,5164,5162,4293,2912,2041,3497,3879,2648,3430,1777,2462,4774,4299,5023,2330,3896,2198,3529,1706,3351,3993,2095,4446,2230,2294,3645,2494,4570,1994,4306,3552,4927,2779,4619,4794,1725,3291,4811,2233,3892,1625,2522,1593,3521,1673,3132,4367,3203,1908,2142,3379,2930,2258,2374,4880,4039,1642,4917,4014,1957,5129,4399,4687,4670,3785,2155,2534,2255,4809,2983,2951,4523,2815,2008,4841,4357,4491,1757,3690,5014,2768,3469,5041,3328,4051,5159,4210,4427,1789,2366,2961,2404,2223,2619,2668,1742,3982,3822,2751,2800,3956,4755,1657,5092,4895,2186,3347,4631,3177,3804,4968,2746,4157,5019,4083,4024,3850,2704,2714,3426,4442,4034,3045,3506,3843,2021,2063,5110,3805,2651,3244,2502,1829,3543,5151,3360,3869,3489,4239,4229,4955,4363,3362,2731,3025,1827,2803,4242,2847,2600,4382,3570,3605,4972,1976,4987,3259,4066,3965,1923,5060,5046,4206,3538,1925,4330,3939,2539,1597,2864,3740,4071,3113,2484,1885,2699,3812,4271,2270,1606,2879,4891,2998,1848,4863,3296,3669,3901,3013,3526,3960,2754,4335,3950,5029,5073,4520,4642,3227,4627,1962,2563,3924,1945,4723,3096,4784,2887,4767,3405,2074,2018,2866,2832,4547,2436,2438,4313,2615,1769,3316,2834,2993,3200,2191,2106,3933,3553,3721,4174,4940,2980,3035,3575,4552,2655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV716-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 14:50:06 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.44/1.48 % [INFO] Parsing done (497ms).
% 2.87/1.50 % [INFO] Running in sequential loop mode.
% 3.44/1.87 % [INFO] eprover registered as external prover.
% 3.44/1.88 % [INFO] Scanning for conjecture ...
% 4.74/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 1572 axioms. Running axiom selection ...
% 6.08/2.58 % [INFO] Axiom selection finished. Selected 1565 axioms (removed 7 axioms).
% 8.10/3.09 % [INFO] Problem is propositional (TPTP CNF).
% 8.52/3.13 % [INFO] Type checking passed.
% 8.52/3.14 % [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 ...
% 84.33/19.53 % External prover 'e' found a proof!
% 84.33/19.53 % [INFO] Killing All external provers ...
% 84.33/19.53 % Time passed: 18981ms (effective reasoning time: 18027ms)
% 84.33/19.55 % Axioms used in derivation (1565): cls_abs__le__zero__iff_0, cls_mult__eq__1__iff_1, cls_Suc__pred_0, cls_divide__le__eq__number__of_9, cls_Suc__Suc__mult__two__diff__two_0, cls_root__cancel_0, cls_mod__Suc__eq__mod__add3_0, cls_even__add_2, cls_add__0__left_0, cls_le__divide__eq_8, cls_add__cancel__end_1, cls_minus__le__iff_0, cls_power__0_0, cls_mult__numeral__1__right_0, cls_le__divide__eq_3, cls_even__sum__nat_2, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_less__divide__eq_3, cls_divide__le__eq__number__of1_9, cls_zero__less__power__eq_1, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_less__iff__diff__less__0_0, cls_fact__mono__nat_0, cls_zero__le__power__iff_2, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_one__le__mult__iff_1, cls_add__pos__nonneg_0, cls_even__difference__nat_4, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_divide__eq__eq_3, cls_eq__add__iff2_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, cls_mult__div__cancel_0, cls_sum__power2__gt__zero__iff_2, cls_neg__0__le__iff__le_1, cls_order__le__less__trans_0, cls_mult__cancel2_0, cls_add__is__1_1, cls_less__diff__iff_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_odd__power__less__zero_0, cls_gb__semiring_Omul__0_0, cls_Suc__inject_0, cls_eq__imp__le_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_le__diff__iff_0, cls_zero__less__divide__iff_5, cls_gb__semiring_Osemiring__rules_I12_J_0, cls_mod__mult__mult1_0, cls_less__divide__eq__number__of1_6, cls_abs__div__pos_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs, cls_zero__le__odd__power_1, cls_abs__if__lattice_0, cls_abs__le__iff_2, cls_less__int__code_I15_J_1, cls_odd__add_1, cls_divide__le__eq_2, cls_mult__imp__le__div__pos_0, cls_divide__pos__pos_0, clsarity_Int__Oint__Int_Onumber, 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, 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_rel__simps_I12_J_0, cls_order__eq__iff_0, cls_divide__less__0__iff_0, cls_div__le__mono_0, cls_gb__semiring_Osemiring__rules_I7_J_0, cls_even__zero__nat_0, cls_even__difference__nat_1, cls_divide__eq__eq__number__of_4, cls_le__add__diff__inverse2_0, cls_abs__of__nonneg_0, cls_Nat_Odiff__diff__eq_0, cls_zero__le__even__power_H_0, cls_le__diff__conv_1, cls_le__minus__self__iff_0, cls_left__add__mult__distrib_0, cls_mult__less__cancel__right__disj_0, cls_divide__self_0, cls_rel__simps_I43_J_1, cls_mult__nonneg__nonpos2_0, cls_power__divides__special_0, cls_sum__squares__eq__zero__iff_0, cls_one__is__add_4, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_left__minus_0, cls_less__special_I1_J_1, cls_square__eq__iff_1, cls_le__divide__eq__number__of1_0, cls_minus__zero_0, cls_power__le__zero__eq__number__of_1, cls_Lim_Ominus__diff__minus_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_mult_Odiff__left_0, clsarity_Int__Oint__Ring__and__Field_Olordered__ring, cls_xt1_I12_J_0, cls_less__int__code_I16_J_0, cls_less__special_I3_J_0, cls_even__even__mod__4__iff_1, clsarity_Int__Oint__Ring__and__Field_Oabs__if, cls_Suc__n__not__n_0, cls_Bit0__Pls_0, cls_fact__add__num__eq__if2__nat_0, cls_divide__le__eq__number__of_4, cls_zero__less__power__eq_5, clsarity_Complex__Ocomplex__Int_Onumber, cls_divide__nonpos__neg_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_nat__mult__div__cancel__disj_0, cls_comp__arith_I112_J_0, cls_number__of__Bit1_0, cls_mult__is__0_2, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_add__increasing2_0, cls_eq__diff__iff_0, cls_gb__semiring_Opwr__pwr_0, cls_divide__numeral__1_0, cls_less__half__sum_0, cls_less__antisym_0, cls_nat__mod__eq__iff_1, cls_divide__less__eq__number__of1_5, cls_le__divide__eq__number__of_6, cls_less__divide__eq__number__of_8, cls_not__sum__squares__lt__zero_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_half_0, cls_nat__lt__two__imp__zero__or__one_0, cls_abs__diff__triangle__ineq_0, cls_mod__by__0_0, cls_add__is__1_2, 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_linorder__neqE_0, cls_divide__1_0, cls_add__strict__right__mono_0, clsarity_Int__Oint__Orderings_Oorder, cls_one__le__mult__iff_0, cls_even__Suc_0, cls_power__increasing_0, cls_power2__less__0_0, cls_minus__one__even__power_0, cls_less__add__Suc2_0, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, cls_divide__le__eq__number__of1_4, clsarity_Int__Oint__Ring__and__Field_Opordered__ring, 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cls_mult__less__cancel__left__disj_3, cls_divide__le__eq__number__of1_1, cls_diff__le__self_0, cls_n__less__m__mult__n_0, cls_zero__less__mult__pos2_0, cls_divide__eq__eq__number__of1_1, cls_mult__left_Ominus_0, cls_nat__less__le_0, cls_divide__left__mono_0, clsarity_Int__Oint__OrderedGroup_Omonoid__mult, cls_mult_Oadd__right_0, cls_mult__1__left_0, cls_nat_Osimps_I3_J_0, cls_frac__eq__eq_1, cls_le__cube_0, cls_abs__number__of_0, cls_div__mult__mult2_0, clsarity_nat__Ring__and__Field_Omult__mono1, cls_diff__add__assoc2_0, cls_mult__le__cancel2_0, cls_le__diff__conv2_1, cls_mod__mult__mult2_0, cls_mod__mult__eq_0, cls_minus__le__iff_1, cls_mult__less__cancel__right__disj_4, cls_le__Suc__ex__iff_1, cls_double__add__less__zero__iff__single__less__zero_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors, cls_eq__add__iff2_0, cls_diff__less__mono2_0, cls_one__less__mult_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_trans__less__add1_0, 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cls_less__minus__self__iff_0, cls_Suc__mod__eq__add3__mod_0, cls_power__inject__base_0, cls_nat__le__add__iff1_1, cls_less__divide__eq__number__of_2, cls_fact__less__mono__nat_0, cls_equation__minus__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring, cls_gb__semiring_Osemiring__rules_I24_J_0, cls_mult_Oprod__diff__prod_0, cls_zmod__simps_I1_J_0, cls_less__SucI_0, cls_nat__mult__le__cancel1_0, cls_div2__Suc__Suc_0, cls_divide__less__eq_9, cls_add__neg__nonpos_0, cls_eq__divide__eq__number__of1_0, cls_mult__divide__mult__cancel__right_0, cls_diff__add__inverse_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add, cls_power__le__zero__eq_4, cls_class__semiring_Osemiring__rules_I24_J_0, cls_abs__leI_0, cls_rel__simps_I47_J_0, cls_class__ringb_Osubr0__iff_1, cls_divide__strict__right__mono_0, clsarity_Complex__Ocomplex__Power_Opower, cls_zero__le__power__eq_1, cls_nat__0__less__mult__iff_2, cls_zero__le__power__eq__number__of_0, cls_not__less0_0, cls_inj__Suc_0, 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cls_div__mult__mult1__if_0, cls_le__less__Suc__eq_1, cls_zero__less__power__nat__eq_2, cls_add__strict__increasing2_0, cls_le__add__diff_0, cls_less__Suc0_1, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_divide__less__eq__number__of1_1, cls_termination__basic__simps_I2_J_0, cls_semiring__div__class_Omod__div__equality_H_0, cls_le__eq__less__or__eq_0, cls_divide__le__eq__number__of1_0, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_gb__semiring_Osemiring__rules_I29_J_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, cls_zero__less__power__eq__number__of_2, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_eq__iff__diff__eq__0_0, cls_mod__mult2__eq_0, cls_odd__pos_0, cls_divide_Ominus_0, cls_less__divide__eq__number__of1_5, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_natgb_Oadd__mul__solve_1, 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_divide__less__eq__number__of_5, cls_square__eq__iff_0, 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_gb__semiring_Osemiring__rules_I11_J_0, cls_mult__minus1__right_0, cls_xt1_I7_J_0, cls_power2__minus_0, cls_nat__mult__less__cancel1_0, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_zero__less__power__eq__number__of_5, cls_linorder__not__less_1, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_not__one__le__zero_0, cls_le__neq__implies__less_0, cls_le__add__iff2_0, cls_mult__less__le__imp__less_0, cls_nat__less__le_1, cls_zero__le__power2_0, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, 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cls_sum__squares__le__zero__iff_0, cls_less__divide__eq__number__of_9, cls_abs__triangle__ineq4_0, cls_less__2__cases_0, cls_add__le__cancel__right_0, cls_mult__right_Odiff_0, cls_le__divide__eq__number__of_0, cls_gb__semiring_Osemiring__rules_I1_J_0, cls_class__semiring_Ogb__semiring__axioms_H_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_mult__eq__1__iff_2, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_abs__of__neg_0, cls_abs__less__iff_1, cls_mult__less__cancel__left__pos_0, cls_nat__add__commute_0, cls_Deriv_Oadd__diff__add_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_div__if_1, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1, cls_add__diff__inverse_0, cls_divide__le__eq__number__of_6, cls_less__divide__eq__number__of1_1, cls_rel__simps_I43_J_0, cls_abs__diff__less__iff_0, cls_zero__le__mult__iff_2, cls_rel__simps_I6_J_0, cls_abs__power2_0, cls_mod__mult__distrib_0, cls_numeral__1__eq__Suc__0_0, cls_divide__le__eq_1, cls_div__Suc__eq__div__add3_0, cls_divide__le__0__1__iff_0
% 84.33/19.55 % No. of inferences in proof: 3137
% 84.33/19.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18981 ms resp. 18027 ms w/o parsing
% 88.02/20.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 88.02/20.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------