%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV712-1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:16 AM UTC 2026
% Result : Unsatisfiable 92.70s 38.77s
% Output : Refutation 94.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 802
% Syntax : Number of formulae : 1627 ( 346 unt; 0 typ; 0 def)
% Number of atoms : 4449 (1169 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 29824 (2601 ~;2822 |; 0 &;24401 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 83 usr; 10 con; 0-6 aty)
% Number of variables : 4337 ( 0 ^;4337 !; 0 ?;4337 :)
% Comments :
%------------------------------------------------------------------------------
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(c_FFT__Mirabelle_OIDFT_decl,type,
c_FFT__Mirabelle_OIDFT: $i > $i > $i > $i ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $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(v_ka_____decl,type,
v_ka____: $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(v_i_____decl,type,
v_i____: $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_Ring__and__Field_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Int_Onumber_decl,type,
class_Int_Onumber: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $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(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $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_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $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_Ono__zero__divisors_decl,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Lattices_Oboolean__algebra_decl,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_decl,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $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__add_decl,type,
class_OrderedGroup_Ocomm__monoid__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(class_Power_Opower_decl,type,
class_Power_Opower: $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_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $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_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Oordered__field_decl,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_decl,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(class_Ring__and__Field_Oring__1_decl,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Int_Oring__char__0_decl,type,
class_Int_Oring__char__0: $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_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(c_Parity_Oeven__odd__class_Oeven_decl,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(c_Groebner__Basis_Ogb__semiring_decl,type,
c_Groebner__Basis_Ogb__semiring: $i > $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Int_OMin_decl,type,
c_Int_OMin: $i ).
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(class_RealVector_Oreal__field_decl,type,
class_RealVector_Oreal__field: $i > $o ).
thf(61,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(892,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)],[61]) ).
thf(379,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(1665,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)],[379]) ).
thf(175,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(1168,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)],[175]) ).
thf(651,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(2336,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)],[651]) ).
thf(473,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1899,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(450,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(1840,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)],[450]) ).
thf(741,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(2559,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)],[741]) ).
thf(649,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(2331,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)],[649]) ).
thf(228,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(1295,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)],[228]) ).
thf(497,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(1956,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)],[497]) ).
thf(334,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(1554,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)],[334]) ).
thf(346,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(1586,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)],[346]) ).
thf(312,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(1501,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)],[312]) ).
thf(5,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(809,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(762,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(2612,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)],[762]) ).
thf(117,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(1024,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)],[117]) ).
thf(443,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1823,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(184,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(1190,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(544,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(2072,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)],[544]) ).
thf(420,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(1767,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)],[420]) ).
thf(204,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(1237,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)],[204]) ).
thf(41,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(846,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(235,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(1315,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)],[235]) ).
thf(719,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(2499,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(689,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(2427,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(139,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(1083,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)],[139]) ).
thf(91,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(962,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)],[91]) ).
thf(508,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(1982,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)],[508]) ).
thf(561,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(2117,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)],[561]) ).
thf(609,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(2231,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)],[609]) ).
thf(320,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(1522,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)],[320]) ).
thf(669,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(2381,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)],[669]) ).
thf(675,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(2395,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)],[675]) ).
thf(784,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(2659,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)],[784]) ).
thf(359,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(1618,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)],[359]) ).
thf(105,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(994,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)],[105]) ).
thf(753,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(2590,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)],[753]) ).
thf(55,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(878,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)],[55]) ).
thf(325,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(1533,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(123,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(1041,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)],[123]) ).
thf(662,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(2363,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)],[662]) ).
thf(189,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(1200,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(413,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(1750,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)],[413]) ).
thf(97,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(977,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)],[97]) ).
thf(483,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(1924,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)],[483]) ).
thf(109,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(1005,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)],[109]) ).
thf(601,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(2210,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(339,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(1569,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)],[339]) ).
thf(489,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(1939,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)],[489]) ).
thf(616,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(2248,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)],[616]) ).
thf(560,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).
thf(2114,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(216,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(1269,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)],[216]) ).
thf(177,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(1173,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)],[177]) ).
thf(306,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(1486,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(282,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(1426,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)],[282]) ).
thf(381,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(1671,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)],[381]) ).
thf(354,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(1608,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)],[354]) ).
thf(162,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(1137,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)],[162]) ).
thf(760,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(2607,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)],[760]) ).
thf(415,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(1756,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)],[415]) ).
thf(530,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(2035,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)],[530]) ).
thf(407,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(1735,plain,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_FFT__Mirabelle_OIFFT ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(461,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(1867,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)],[461]) ).
thf(642,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(2316,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)],[642]) ).
thf(219,axiom,
( c_Int_OPls
= ( c_Int_OPls @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_1) ).
thf(1275,plain,
( c_Int_OPls
= ( c_Int_OPls @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(463,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(1872,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)],[463]) ).
thf(202,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(1233,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)],[202]) ).
thf(10,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(814,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(748,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(2580,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)],[748]) ).
thf(83,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(945,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)],[83]) ).
thf(76,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(930,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)],[76]) ).
thf(294,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(1458,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)],[294]) ).
thf(310,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(1497,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(394,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(1705,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)],[394]) ).
thf(709,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(2476,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)],[709]) ).
thf(213,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(1260,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)],[213]) ).
thf(481,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(1919,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)],[481]) ).
thf(702,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(2459,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)],[702]) ).
thf(132,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(1063,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)],[132]) ).
thf(496,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(1954,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)],[496]) ).
thf(252,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(1354,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)],[252]) ).
thf(574,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(2146,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)],[574]) ).
thf(24,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(829,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(448,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(1835,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)],[448]) ).
thf(655,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(2348,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)],[655]) ).
thf(267,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(1391,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)],[267]) ).
thf(288,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(1441,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)],[288]) ).
thf(125,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(1046,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)],[125]) ).
thf(356,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(1613,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(487,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(1935,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)],[487]) ).
thf(369,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(1645,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(254,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(1359,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)],[254]) ).
thf(302,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(1475,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)],[302]) ).
thf(726,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(2516,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)],[726]) ).
thf(503,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(1967,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)],[503]) ).
thf(435,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(1803,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(731,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(2531,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)],[731]) ).
thf(206,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(1243,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)],[206]) ).
thf(158,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(1127,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(737,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(2548,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)],[737]) ).
thf(524,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(2020,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)],[524]) ).
thf(36,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(841,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(569,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(2136,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)],[569]) ).
thf(476,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(1904,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)],[476]) ).
thf(361,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(1623,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)],[361]) ).
thf(211,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(1254,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)],[211]) ).
thf(648,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(2328,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)],[648]) ).
thf(787,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(2667,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)],[787]) ).
thf(652,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(2339,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)],[652]) ).
thf(477,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(1907,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)],[477]) ).
thf(604,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(2217,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)],[604]) ).
thf(71,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(917,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)],[71]) ).
thf(793,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(2682,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)],[793]) ).
thf(185,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(1191,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)],[185]) ).
thf(512,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(1992,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)],[512]) ).
thf(296,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(1462,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)],[296]) ).
thf(1,negated_conjecture,
( ( v_i____ @ ( 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 ) ) @ ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(803,plain,
( ( v_i____ @ ( 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 ) ) @ ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(804,plain,
( ( v_i____ @ ( 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 ) ) @ ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(polarity_switch,[status(thm)],[803]) ).
thf(805,plain,
( ( v_i____ @ ( 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 ) ) @ ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(lifteq,[status(thm)],[804]) ).
thf(2703,plain,
( ( ( v_i____ @ ( 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 ) ) @ ( v_i____ @ ( 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 ) )
!= ( v_i____ @ ( 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 ) @ ( v_i____ @ ( 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 ) ) )
| ( ( v_i____ @ ( 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 ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) )
!= ( v_i____ @ ( 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 ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) ) ) ),
inference(simp,[status(thm)],[805]) ).
thf(417,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(1760,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)],[417]) ).
thf(377,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(1660,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)],[377]) ).
thf(239,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(1323,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)],[239]) ).
thf(33,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(838,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(342,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(1577,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)],[342]) ).
thf(293,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(1455,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)],[293]) ).
thf(742,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(2562,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)],[742]) ).
thf(714,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(2488,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)],[714]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(949,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(745,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(2571,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)],[745]) ).
thf(659,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(2356,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)],[659]) ).
thf(44,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(853,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)],[44]) ).
thf(262,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(1379,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)],[262]) ).
thf(773,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(2635,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(423,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(1773,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)],[423]) ).
thf(440,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(1815,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)],[440]) ).
thf(255,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(1362,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)],[255]) ).
thf(331,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(1545,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)],[331]) ).
thf(686,axiom,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).
thf(2420,plain,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(482,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(1922,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)],[482]) ).
thf(13,axiom,
tc_Int_Oint @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(817,plain,
tc_Int_Oint @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(797,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(2691,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(65,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(902,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)],[65]) ).
thf(237,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(1319,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(51,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(870,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(270,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(1398,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)],[270]) ).
thf(56,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(881,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)],[56]) ).
thf(464,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(1875,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)],[464]) ).
thf(425,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(1778,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)],[425]) ).
thf(398,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(1714,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)],[398]) ).
thf(556,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(2105,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)],[556]) ).
thf(550,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(2090,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)],[550]) ).
thf(259,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(1373,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)],[259]) ).
thf(151,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(1109,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)],[151]) ).
thf(620,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(2259,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)],[620]) ).
thf(780,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(2650,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)],[780]) ).
thf(29,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
thf(834,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(79,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(937,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)],[79]) ).
thf(618,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(2254,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)],[618]) ).
thf(2,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(806,plain,
tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(522,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(2017,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)],[522]) ).
thf(701,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(2456,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)],[701]) ).
thf(518,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(2007,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)],[518]) ).
thf(587,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(2178,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)],[587]) ).
thf(606,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(2222,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)],[606]) ).
thf(307,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(1489,plain,
! [A: $i] :
( ( A = c_Int_OMin )
| ( ( A @ c_Int_OBit1 )
!= c_Int_OMin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(278,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(1415,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)],[278]) ).
thf(764,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(2616,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(492,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(1946,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)],[492]) ).
thf(279,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(1418,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)],[279]) ).
thf(698,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(2451,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)],[698]) ).
thf(611,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(2236,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(458,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(1858,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)],[458]) ).
thf(460,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(1864,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)],[460]) ).
thf(563,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(2122,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)],[563]) ).
thf(181,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(1183,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)],[181]) ).
thf(222,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(1283,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)],[222]) ).
thf(127,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(1051,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)],[127]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(821,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(539,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(2058,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)],[539]) ).
thf(261,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(1377,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)],[261]) ).
thf(629,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(2281,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)],[629]) ).
thf(592,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(2190,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)],[592]) ).
thf(290,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(1447,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)],[290]) ).
thf(665,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(2371,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(322,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(1526,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)],[322]) ).
thf(251,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(1351,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)],[251]) ).
thf(516,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(2002,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)],[516]) ).
thf(190,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(1201,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)],[190]) ).
thf(351,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(1600,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)],[351]) ).
thf(577,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(2154,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)],[577]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(866,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(468,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(1886,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)],[468]) ).
thf(432,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(1796,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)],[432]) ).
thf(135,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(1072,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)],[135]) ).
thf(614,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(2242,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)],[614]) ).
thf(102,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(988,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)],[102]) ).
thf(631,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(2286,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)],[631]) ).
thf(775,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(2639,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)],[775]) ).
thf(555,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(2103,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)],[555]) ).
thf(274,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(1405,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)],[274]) ).
thf(391,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(1696,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)],[391]) ).
thf(751,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2586,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(372,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(1651,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)],[372]) ).
thf(82,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(942,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)],[82]) ).
thf(599,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(2204,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)],[599]) ).
thf(74,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(925,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)],[74]) ).
thf(232,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(1306,plain,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(581,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(2164,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)],[581]) ).
thf(169,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(1153,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)],[169]) ).
thf(6,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(810,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(244,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I40_J_0) ).
thf(1336,plain,
c_Int_OMin != c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1337,plain,
c_Int_OMin != c_Int_OPls,
inference(polarity_switch,[status(thm)],[1336]) ).
thf(1338,plain,
c_Int_OMin != c_Int_OPls,
inference(lifteq,[status(thm)],[1337]) ).
thf(427,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(1783,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)],[427]) ).
thf(639,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(2307,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)],[639]) ).
thf(718,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(2496,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)],[718]) ).
thf(405,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(1730,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)],[405]) ).
thf(746,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(2574,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)],[746]) ).
thf(287,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(1438,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)],[287]) ).
thf(300,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(1470,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)],[300]) ).
thf(395,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(1708,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)],[395]) ).
thf(540,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(2061,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)],[540]) ).
thf(515,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(2000,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)],[515]) ).
thf(366,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(1636,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)],[366]) ).
thf(681,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(2409,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)],[681]) ).
thf(143,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(1091,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)],[143]) ).
thf(690,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(2428,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(319,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(1519,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)],[319]) ).
thf(344,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(1580,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)],[344]) ).
thf(47,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(862,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)],[47]) ).
thf(568,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(2133,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)],[568]) ).
thf(16,axiom,
tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
thf(820,plain,
tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(444,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(1824,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)],[444]) ).
thf(730,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(2528,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)],[730]) ).
thf(521,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(2015,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)],[521]) ).
thf(265,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(1387,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)],[265]) ).
thf(474,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(1900,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)],[474]) ).
thf(68,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(910,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)],[68]) ).
thf(89,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(957,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)],[89]) ).
thf(198,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(1223,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)],[198]) ).
thf(20,axiom,
tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
thf(825,plain,
tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(247,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(1343,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)],[247]) ).
thf(529,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(2032,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)],[529]) ).
thf(11,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(815,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(467,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(1883,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)],[467]) ).
thf(336,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I37_J_0) ).
thf(1560,plain,
c_Int_OPls != c_Int_OMin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(695,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(2445,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)],[695]) ).
thf(691,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(2433,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)],[691]) ).
thf(743,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(2565,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)],[743]) ).
thf(179,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(1178,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)],[179]) ).
thf(387,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(1687,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(588,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(2181,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)],[588]) ).
thf(647,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(2327,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(654,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(2345,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)],[654]) ).
thf(96,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(974,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)],[96]) ).
thf(704,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(2464,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(42,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(847,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)],[42]) ).
thf(120,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(1032,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)],[120]) ).
thf(449,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(1837,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)],[449]) ).
thf(352,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(1602,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)],[352]) ).
thf(256,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(1365,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)],[256]) ).
thf(770,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(2628,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)],[770]) ).
thf(788,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(2670,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)],[788]) ).
thf(597,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(2200,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)],[597]) ).
thf(761,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(2609,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)],[761]) ).
thf(25,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(830,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(193,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(1210,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)],[193]) ).
thf(374,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(1656,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)],[374]) ).
thf(187,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(1195,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)],[187]) ).
thf(602,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(2211,plain,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(275,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(1407,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)],[275]) ).
thf(641,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(2313,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)],[641]) ).
thf(159,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(1128,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)],[159]) ).
thf(716,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(2492,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)],[716]) ).
thf(365,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(1634,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)],[365]) ).
thf(608,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(2228,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)],[608]) ).
thf(559,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(2112,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)],[559]) ).
thf(226,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(1291,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)],[226]) ).
thf(409,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(1740,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)],[409]) ).
thf(478,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(1910,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)],[478]) ).
thf(37,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(842,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(781,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(2653,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)],[781]) ).
thf(149,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(1106,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(329,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(1541,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)],[329]) ).
thf(747,axiom,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
thf(2577,plain,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(799,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(2694,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)],[799]) ).
thf(145,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(1096,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)],[145]) ).
thf(771,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(2631,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)],[771]) ).
thf(733,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(2537,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)],[733]) ).
thf(155,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(1118,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)],[155]) ).
thf(624,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(2268,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)],[624]) ).
thf(615,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(2245,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)],[615]) ).
thf(250,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(1350,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)],[250]) ).
thf(348,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(1592,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)],[348]) ).
thf(636,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(2300,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)],[636]) ).
thf(53,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(874,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)],[53]) ).
thf(164,axiom,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I42_J_0) ).
thf(1141,plain,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1142,plain,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
inference(polarity_switch,[status(thm)],[1141]) ).
thf(1143,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
inference(lifteq,[status(thm)],[1142]) ).
thf(418,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(1762,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)],[418]) ).
thf(554,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(2100,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)],[554]) ).
thf(326,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(1534,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)],[326]) ).
thf(431,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(1794,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)],[431]) ).
thf(260,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(1375,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)],[260]) ).
thf(156,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(1121,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)],[156]) ).
thf(152,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(1111,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)],[152]) ).
thf(504,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(1970,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)],[504]) ).
thf(98,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(980,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)],[98]) ).
thf(798,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(2692,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)],[798]) ).
thf(311,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(1498,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)],[311]) ).
thf(525,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(2023,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)],[525]) ).
thf(645,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(2323,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)],[645]) ).
thf(136,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(1075,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)],[136]) ).
thf(488,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(1937,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)],[488]) ).
thf(469,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(1889,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)],[469]) ).
thf(94,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(970,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)],[94]) ).
thf(57,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(884,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)],[57]) ).
thf(241,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(1329,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)],[241]) ).
thf(500,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(1964,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(490,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(1942,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)],[490]) ).
thf(376,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(1659,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Parity_Oeven__odd__class_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(281,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(1424,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)],[281]) ).
thf(700,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(2455,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(595,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(2196,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)],[595]) ).
thf(451,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(1842,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)],[451]) ).
thf(585,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(2172,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)],[585]) ).
thf(438,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(1810,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)],[438]) ).
thf(430,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(1791,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)],[430]) ).
thf(557,axiom,
( c_Int_OMin
= ( c_Int_OMin @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_1) ).
thf(2108,plain,
( c_Int_OMin
= ( c_Int_OMin @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(531,axiom,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit1__Min_0) ).
thf(2038,plain,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(114,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(1016,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)],[114]) ).
thf(192,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(1207,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)],[192]) ).
thf(643,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(2317,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)],[643]) ).
thf(170,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(1155,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)],[170]) ).
thf(32,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(837,plain,
tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(153,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(1114,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)],[153]) ).
thf(229,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(1297,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)],[229]) ).
thf(324,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(1530,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)],[324]) ).
thf(160,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(1131,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)],[160]) ).
thf(380,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(1668,plain,
! [A: $i] :
( ( A = c_Int_OPls )
| ( ( A @ c_Int_OBit0 )
!= c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(486,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(1932,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)],[486]) ).
thf(705,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(2465,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)],[705]) ).
thf(100,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(984,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)],[100]) ).
thf(433,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(1799,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)],[433]) ).
thf(509,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(1984,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)],[509]) ).
thf(712,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(2482,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)],[712]) ).
thf(401,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(1720,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)],[401]) ).
thf(507,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(1979,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)],[507]) ).
thf(626,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(2272,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)],[626]) ).
thf(571,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(2140,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)],[571]) ).
thf(268,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(1393,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)],[268]) ).
thf(321,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(1525,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(424,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(1776,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)],[424]) ).
thf(214,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(1263,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)],[214]) ).
thf(106,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(997,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)],[106]) ).
thf(565,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(2125,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)],[565]) ).
thf(146,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(1099,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)],[146]) ).
thf(168,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(1150,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)],[168]) ).
thf(303,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(1478,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)],[303]) ).
thf(727,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(2519,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)],[727]) ).
thf(215,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(1266,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)],[215]) ).
thf(672,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(2387,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)],[672]) ).
thf(201,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(1231,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)],[201]) ).
thf(108,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(1002,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)],[108]) ).
thf(455,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(1852,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)],[455]) ).
thf(243,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(1333,plain,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(236,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(1318,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(802,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(2702,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(533,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(2043,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)],[533]) ).
thf(337,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(1563,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)],[337]) ).
thf(183,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(1187,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)],[183]) ).
thf(378,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(1663,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)],[378]) ).
thf(765,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(2617,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)],[765]) ).
thf(59,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(888,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)],[59]) ).
thf(406,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(1732,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)],[406]) ).
thf(772,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
thf(2634,plain,
tc_Complex_Ocomplex @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(2706,plain,
( ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) )
| ( ( v_i____ @ ( 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 ) )
!= ( v_i____ @ ( 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 ) ) )
| ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) )
| ( ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus )
!= ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus ) ) ),
inference(simp,[status(thm)],[2703]) ).
thf(2728,plain,
( ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) )
| ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) ),
inference(simp,[status(thm)],[2706]) ).
thf(2736,plain,
( ( ( v_i____ @ ( 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 ) )
!= ( v_i____ @ ( 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 ) ) )
| ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) )
| ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[2728]) ).
thf(2739,plain,
( ( v_i____ != v_i____ )
| ( ( 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 ) )
!= ( 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 ) ) )
| ( v_i____ != v_i____ )
| ( ( 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 ) ) ) ) )
!= ( 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 ) )
!= ( 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____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) ),
inference(simp,[status(thm)],[2736]) ).
thf(2742,plain,
( ( ( 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 ) )
!= ( 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 ) ) )
| ( ( 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 ) ) ) ) )
!= ( 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_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) ),
inference(simp,[status(thm)],[2739]) ).
thf(2746,plain,
( ( ( 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 ) ) ) ) )
!= ( 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____ != v_ka____ )
| ( ( 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 ) ) ) ) )
!= ( 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_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) ),
inference(simp,[status(thm)],[2742]) ).
thf(2749,plain,
( ( ( 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 ) ) ) ) )
!= ( 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_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) ),
inference(simp,[status(thm)],[2746]) ).
thf(285,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(1434,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)],[285]) ).
thf(457,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1857,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(453,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(1846,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)],[453]) ).
thf(128,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(1054,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)],[128]) ).
thf(224,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(1286,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)],[224]) ).
thf(121,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(1035,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)],[121]) ).
thf(664,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(2368,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)],[664]) ).
thf(118,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(1026,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)],[118]) ).
thf(174,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(1167,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(778,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(2645,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)],[778]) ).
thf(591,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(2189,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(87,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(953,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)],[87]) ).
thf(785,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( 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(2662,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)],[785]) ).
thf(182,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(1185,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)],[182]) ).
thf(371,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(1648,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)],[371]) ).
thf(683,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(2413,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)],[683]) ).
thf(791,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(2677,plain,
! [A: $i] :
( ( c_Int_OMin = A )
| ( c_Int_OMin
!= ( A @ c_Int_OBit1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(19,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(824,plain,
tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(305,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(1483,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(218,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(1273,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)],[218]) ).
thf(412,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(1747,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)],[412]) ).
thf(45,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(856,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)],[45]) ).
thf(758,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(2602,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)],[758]) ).
thf(364,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(1631,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)],[364]) ).
thf(92,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(965,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)],[92]) ).
thf(404,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1727,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(316,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(1510,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)],[316]) ).
thf(166,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(1146,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)],[166]) ).
thf(633,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(2292,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)],[633]) ).
thf(498,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(1959,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)],[498]) ).
thf(740,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(2556,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)],[740]) ).
thf(148,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(1103,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)],[148]) ).
thf(627,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(2275,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)],[627]) ).
thf(575,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(2149,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)],[575]) ).
thf(332,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(1548,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)],[332]) ).
thf(484,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(1927,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)],[484]) ).
thf(527,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(2028,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(349,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(1595,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)],[349]) ).
thf(15,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(819,plain,
tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(66,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(904,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)],[66]) ).
thf(447,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(1833,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)],[447]) ).
thf(2705,plain,
( ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) )
| ( ( v_i____ @ ( 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 ) )
!= ( v_i____ @ ( 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 ) ) )
| ( ( v_i____ @ ( 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 ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) )
!= ( v_i____ @ ( 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 ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) ) ) ),
inference(simp,[status(thm)],[2703]) ).
thf(2727,plain,
( ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) )
| ( ( v_i____ @ ( 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 ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) )
!= ( v_i____ @ ( 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 ) @ ( tc_Complex_Ocomplex @ c_HOL_Oplus__class_Oplus @ hAPP ) ) ) ),
inference(simp,[status(thm)],[2705]) ).
thf(480,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(1916,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)],[480]) ).
thf(535,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(2048,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)],[535]) ).
thf(607,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(2225,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)],[607]) ).
thf(358,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(1615,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)],[358]) ).
thf(38,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
thf(843,plain,
tc_Int_Oint @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(729,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(2525,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)],[729]) ).
thf(674,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(2393,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)],[674]) ).
thf(485,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(1929,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)],[485]) ).
thf(744,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(2568,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)],[744]) ).
thf(21,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(826,plain,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(272,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(1403,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(501,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(1965,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(157,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(1124,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)],[157]) ).
thf(199,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(1226,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)],[199]) ).
thf(428,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(1786,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)],[428]) ).
thf(528,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(2029,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)],[528]) ).
thf(234,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(1312,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)],[234]) ).
thf(514,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(1997,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)],[514]) ).
thf(694,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(2442,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)],[694]) ).
thf(688,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(2425,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)],[688]) ).
thf(660,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(2358,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)],[660]) ).
thf(383,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(1675,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)],[383]) ).
thf(283,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(1428,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)],[283]) ).
thf(580,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(2161,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)],[580]) ).
thf(163,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(1139,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)],[163]) ).
thf(313,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(1503,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)],[313]) ).
thf(217,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(1271,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)],[217]) ).
thf(258,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(1371,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)],[258]) ).
thf(130,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(1058,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)],[130]) ).
thf(150,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(1107,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)],[150]) ).
thf(419,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(1765,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)],[419]) ).
thf(142,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1090,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(472,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(1897,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)],[472]) ).
thf(72,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(919,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)],[72]) ).
thf(297,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(1464,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)],[297]) ).
thf(708,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(2474,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)],[708]) ).
thf(84,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(947,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)],[84]) ).
thf(724,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(2510,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)],[724]) ).
thf(661,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(2361,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)],[661]) ).
thf(562,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(2119,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)],[562]) ).
thf(26,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
thf(831,plain,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(710,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(2478,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(777,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(2642,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)],[777]) ).
thf(126,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(1048,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)],[126]) ).
thf(308,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(1492,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)],[308]) ).
thf(2115,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(polarity_switch,[status(thm)],[2114]) ).
thf(2116,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(lifteq,[status(thm)],[2115]) ).
thf(124,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(1043,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)],[124]) ).
thf(340,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(1571,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)],[340]) ).
thf(178,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(1175,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)],[178]) ).
thf(548,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(2084,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)],[548]) ).
thf(603,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(2214,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)],[603]) ).
thf(684,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(2415,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)],[684]) ).
thf(471,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(1894,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)],[471]) ).
thf(687,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(2422,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)],[687]) ).
thf(154,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(1117,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(341,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(1574,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)],[341]) ).
thf(436,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I45_J_0) ).
thf(1806,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(1011,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(249,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1349,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(553,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(2097,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)],[553]) ).
thf(103,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(990,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)],[103]) ).
thf(619,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(2257,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)],[619]) ).
thf(347,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(1589,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)],[347]) ).
thf(402,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(1722,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)],[402]) ).
thf(165,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(1144,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)],[165]) ).
thf(668,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(2378,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)],[668]) ).
thf(389,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(1690,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)],[389]) ).
thf(60,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(890,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)],[60]) ).
thf(7,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
thf(811,plain,
tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(465,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(1877,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)],[465]) ).
thf(335,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(1557,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)],[335]) ).
thf(768,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2625,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(12,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(816,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(172,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(1162,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)],[172]) ).
thf(696,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(2446,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)],[696]) ).
thf(263,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(1381,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)],[263]) ).
thf(703,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(2461,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)],[703]) ).
thf(442,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(1820,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)],[442]) ).
thf(388,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(1688,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)],[388]) ).
thf(526,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(2025,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)],[526]) ).
thf(138,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(1080,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)],[138]) ).
thf(245,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(1339,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(759,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(2605,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)],[759]) ).
thf(119,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(1029,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)],[119]) ).
thf(62,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(895,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(735,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(2542,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)],[735]) ).
thf(295,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(1460,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)],[295]) ).
thf(632,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(2289,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)],[632]) ).
thf(116,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(1022,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)],[116]) ).
thf(786,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(2664,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)],[786]) ).
thf(628,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(2278,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)],[628]) ).
thf(739,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(2553,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)],[739]) ).
thf(77,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(932,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)],[77]) ).
thf(131,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(1061,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)],[131]) ).
thf(495,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(1952,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)],[495]) ).
thf(663,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(2365,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)],[663]) ).
thf(90,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(959,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)],[90]) ).
thf(101,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(986,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)],[101]) ).
thf(637,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(2303,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)],[637]) ).
thf(578,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(2156,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)],[578]) ).
thf(600,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(2207,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)],[600]) ).
thf(73,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(922,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)],[73]) ).
thf(505,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(1973,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)],[505]) ).
thf(543,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(2069,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)],[543]) ).
thf(722,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(2506,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(69,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(912,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)],[69]) ).
thf(176,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(1171,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)],[176]) ).
thf(545,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(2075,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)],[545]) ).
thf(685,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(2418,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)],[685]) ).
thf(269,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(1396,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)],[269]) ).
thf(693,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(2439,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)],[693]) ).
thf(678,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(2401,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)],[678]) ).
thf(392,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(1699,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)],[392]) ).
thf(194,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(1213,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)],[194]) ).
thf(22,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(827,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(536,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(2051,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)],[536]) ).
thf(738,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(2550,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)],[738]) ).
thf(207,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(1245,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)],[207]) ).
thf(711,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(2481,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(133,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(1066,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)],[133]) ).
thf(766,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(2620,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)],[766]) ).
thf(50,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(868,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)],[50]) ).
thf(754,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(2592,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)],[754]) ).
thf(107,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(1000,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)],[107]) ).
thf(2751,plain,
( ( tc_nat != tc_nat )
| ( tc_Complex_Ocomplex != tc_Complex_Ocomplex )
| ( tc_nat != 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 ) ) ) ) )
!= ( 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____ != v_a____ )
| ( ( v_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) ),
inference(simp,[status(thm)],[2749]) ).
thf(2752,plain,
( ( ( 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 ) ) ) ) )
!= ( 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_i____ @ ( 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 ) ) )
!= ( v_i____ @ ( 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 ) ) ) ),
inference(simp,[status(thm)],[2751]) ).
thf(673,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(2390,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)],[673]) ).
thf(209,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(1250,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)],[209]) ).
thf(277,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(1413,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)],[277]) ).
thf(362,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(1626,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)],[362]) ).
thf(612,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(2239,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)],[612]) ).
thf(345,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(1583,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)],[345]) ).
thf(437,axiom,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(1809,plain,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(763,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(2614,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)],[763]) ).
thf(298,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(1467,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(707,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(2471,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)],[707]) ).
thf(75,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(927,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)],[75]) ).
thf(161,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(1134,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)],[161]) ).
thf(650,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(2333,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)],[650]) ).
thf(756,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(2597,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)],[756]) ).
thf(537,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(2054,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)],[537]) ).
thf(493,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(1948,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(416,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(1758,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)],[416]) ).
thf(173,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(1165,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)],[173]) ).
thf(1166,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(polarity_switch,[status(thm)],[1165]) ).
thf(721,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(2503,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)],[721]) ).
thf(386,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(1684,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)],[386]) ).
thf(220,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(1277,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)],[220]) ).
thf(610,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(2234,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)],[610]) ).
thf(697,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(2449,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)],[697]) ).
thf(8,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(812,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(794,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(2684,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)],[794]) ).
thf(598,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(2202,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)],[598]) ).
thf(80,axiom,
tc_Int_Oint @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(939,plain,
tc_Int_Oint @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(246,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(1340,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)],[246]) ).
thf(93,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(968,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)],[93]) ).
thf(180,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(1181,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)],[180]) ).
thf(18,axiom,
tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
thf(823,plain,
tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(31,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
thf(836,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(333,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(1551,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)],[333]) ).
thf(725,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(2513,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)],[725]) ).
thf(422,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(1770,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)],[422]) ).
thf(499,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(1961,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)],[499]) ).
thf(676,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(2397,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(593,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(2192,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)],[593]) ).
thf(353,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(1605,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)],[353]) ).
thf(414,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(1753,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)],[414]) ).
thf(318,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(1516,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)],[318]) ).
thf(350,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(1598,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)],[350]) ).
thf(355,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(1611,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)],[355]) ).
thf(667,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(2375,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)],[667]) ).
thf(410,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(1743,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(271,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(1400,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)],[271]) ).
thf(338,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(1566,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)],[338]) ).
thf(520,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(2012,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)],[520]) ).
thf(257,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(1368,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)],[257]) ).
thf(586,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(2175,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)],[586]) ).
thf(551,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(2092,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)],[551]) ).
thf(399,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(1716,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(582,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(2165,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)],[582]) ).
thf(122,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(1038,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)],[122]) ).
thf(35,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(840,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(203,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(1235,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)],[203]) ).
thf(446,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(1830,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)],[446]) ).
thf(140,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(1085,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)],[140]) ).
thf(343,axiom,
tc_nat @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(1579,plain,
tc_nat @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(706,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(2468,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)],[706]) ).
thf(782,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(2656,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)],[782]) ).
thf(397,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(1711,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)],[397]) ).
thf(230,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(1300,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)],[230]) ).
thf(292,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(1452,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)],[292]) ).
thf(796,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(2688,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)],[796]) ).
thf(605,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(2219,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(566,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(2128,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)],[566]) ).
thf(328,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(1538,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)],[328]) ).
thf(86,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(951,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)],[86]) ).
thf(736,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(2545,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)],[736]) ).
thf(4,axiom,
tc_Int_Oint @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
thf(808,plain,
tc_Int_Oint @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(223,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1285,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(196,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(1218,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)],[196]) ).
thf(658,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(2354,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)],[658]) ).
thf(67,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(907,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)],[67]) ).
thf(330,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(1543,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)],[330]) ).
thf(434,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(1802,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(393,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(1702,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)],[393]) ).
thf(197,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(1221,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)],[197]) ).
thf(573,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(2145,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(644,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(2320,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)],[644]) ).
thf(48,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(864,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)],[48]) ).
thf(144,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(1094,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)],[144]) ).
thf(110,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(1008,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)],[110]) ).
thf(750,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(2584,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)],[750]) ).
thf(46,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(859,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)],[46]) ).
thf(205,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(1240,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)],[205]) ).
thf(790,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(2675,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)],[790]) ).
thf(538,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(2056,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)],[538]) ).
thf(273,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(1404,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)],[273]) ).
thf(682,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(2411,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)],[682]) ).
thf(720,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(2500,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)],[720]) ).
thf(454,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(1849,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)],[454]) ).
thf(212,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(1257,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)],[212]) ).
thf(327,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(1536,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)],[327]) ).
thf(400,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(1717,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)],[400]) ).
thf(623,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(2266,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)],[623]) ).
thf(54,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(876,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)],[54]) ).
thf(40,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
thf(845,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(280,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(1421,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)],[280]) ).
thf(534,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(2045,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)],[534]) ).
thf(502,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1966,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(800,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(2696,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)],[800]) ).
thf(494,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(1949,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)],[494]) ).
thf(441,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(1817,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)],[441]) ).
thf(594,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(2194,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)],[594]) ).
thf(373,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(1654,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)],[373]) ).
thf(646,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(2325,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)],[646]) ).
thf(715,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(2490,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)],[715]) ).
thf(783,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(2658,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(769,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(2626,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)],[769]) ).
thf(657,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(2352,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)],[657]) ).
thf(171,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(1157,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(546,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(2078,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)],[546]) ).
thf(479,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(1913,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)],[479]) ).
thf(640,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(2310,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)],[640]) ).
thf(452,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(1844,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)],[452]) ).
thf(426,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(1781,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(195,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(1216,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)],[195]) ).
thf(558,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(2110,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)],[558]) ).
thf(111,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(1010,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(266,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(1390,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(638,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(2305,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)],[638]) ).
thf(653,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(2342,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)],[653]) ).
thf(225,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(1289,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)],[225]) ).
thf(39,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(844,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(370,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(1646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( 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)],[370]) ).
thf(240,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(1326,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)],[240]) ).
thf(210,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(1253,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(583,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(2167,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)],[583]) ).
thf(630,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(2283,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)],[630]) ).
thf(63,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_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(896,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_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(367,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(1639,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)],[367]) ).
thf(617,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(2251,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)],[617]) ).
thf(680,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(2406,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)],[680]) ).
thf(315,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(1508,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)],[315]) ).
thf(147,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(1101,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)],[147]) ).
thf(411,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(1745,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)],[411]) ).
thf(456,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(1854,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)],[456]) ).
thf(567,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(2130,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)],[567]) ).
thf(9,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(813,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(755,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(2594,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)],[755]) ).
thf(363,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(1629,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)],[363]) ).
thf(517,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(2004,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)],[517]) ).
thf(576,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(2152,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)],[576]) ).
thf(621,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(2262,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)],[621]) ).
thf(547,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(2081,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)],[547]) ).
thf(670,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(2384,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(70,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(914,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)],[70]) ).
thf(677,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(2399,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)],[677]) ).
thf(779,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(2648,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)],[779]) ).
thf(227,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1294,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(596,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(2198,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)],[596]) ).
thf(542,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(2066,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)],[542]) ).
thf(186,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(1193,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)],[186]) ).
thf(137,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(1077,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)],[137]) ).
thf(317,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(1513,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)],[317]) ).
thf(64,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(899,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)],[64]) ).
thf(767,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(2623,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)],[767]) ).
thf(513,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(1994,plain,
! [A: $i] :
( ( c_Int_OPls = A )
| ( c_Int_OPls
!= ( A @ c_Int_OBit0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(523,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(2019,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(357,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_True_0) ).
thf(1614,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)],[357]) ).
thf(519,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(2009,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)],[519]) ).
thf(459,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(1861,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)],[459]) ).
thf(792,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(2680,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)],[792]) ).
thf(589,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(2183,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)],[589]) ).
thf(552,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(2095,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)],[552]) ).
thf(27,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
thf(832,plain,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(634,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(2294,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)],[634]) ).
thf(233,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(1309,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)],[233]) ).
thf(717,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(2494,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)],[717]) ).
thf(289,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(1444,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)],[289]) ).
thf(572,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(2142,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)],[572]) ).
thf(564,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(2123,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)],[564]) ).
thf(368,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(1642,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)],[368]) ).
thf(732,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(2534,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)],[732]) ).
thf(28,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
thf(833,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(200,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(1229,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)],[200]) ).
thf(14,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(818,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(728,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(2522,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)],[728]) ).
thf(208,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(1248,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)],[208]) ).
thf(304,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(1480,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)],[304]) ).
thf(403,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(1725,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)],[403]) ).
thf(221,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(1280,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)],[221]) ).
thf(671,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(2385,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)],[671]) ).
thf(384,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(1678,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)],[384]) ).
thf(30,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(835,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(752,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(2587,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)],[752]) ).
thf(231,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(1303,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)],[231]) ).
thf(510,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(1986,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)],[510]) ).
thf(323,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(1527,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)],[323]) ).
thf(167,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(1148,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)],[167]) ).
thf(382,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(1673,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)],[382]) ).
thf(774,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(2636,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)],[774]) ).
thf(286,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(1436,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)],[286]) ).
thf(511,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(1989,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)],[511]) ).
thf(309,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(1495,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)],[309]) ).
thf(375,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(1657,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)],[375]) ).
thf(590,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(2186,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)],[590]) ).
thf(3,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(807,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(390,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(1693,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)],[390]) ).
thf(276,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(1410,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)],[276]) ).
thf(679,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(2404,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)],[679]) ).
thf(470,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(1891,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)],[470]) ).
thf(23,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
thf(828,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(301,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(1473,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)],[301]) ).
thf(532,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(2040,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)],[532]) ).
thf(88,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(955,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)],[88]) ).
thf(58,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(886,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)],[58]) ).
thf(129,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(1056,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)],[129]) ).
thf(429,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(1789,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)],[429]) ).
thf(396,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(1710,plain,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(188,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(1197,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)],[188]) ).
thf(248,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(1346,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)],[248]) ).
thf(541,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(2063,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)],[541]) ).
thf(34,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
thf(839,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(613,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(2241,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(579,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(2159,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)],[579]) ).
thf(445,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(1827,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)],[445]) ).
thf(506,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(1976,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)],[506]) ).
thf(104,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(992,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)],[104]) ).
thf(475,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(1902,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)],[475]) ).
thf(801,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(2699,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)],[801]) ).
thf(52,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(871,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)],[52]) ).
thf(666,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(2372,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)],[666]) ).
thf(570,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(2138,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)],[570]) ).
thf(757,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(2600,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)],[757]) ).
thf(264,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(1384,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)],[264]) ).
thf(713,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(2485,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)],[713]) ).
thf(622,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(2265,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)],[622]) ).
thf(115,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(1019,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)],[115]) ).
thf(253,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(1357,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)],[253]) ).
thf(749,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(2583,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_Suc @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(822,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
inference(cnf,[status(esa)],[821]) ).
thf(723,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(2507,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(734,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(2539,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)],[734]) ).
thf(43,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(850,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)],[43]) ).
thf(795,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(2687,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(99,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(982,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)],[99]) ).
thf(466,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(1880,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)],[466]) ).
thf(284,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(1431,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)],[284]) ).
thf(314,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(1505,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)],[314]) ).
thf(625,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(2270,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)],[625]) ).
thf(360,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(1621,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)],[360]) ).
thf(242,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(1331,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)],[242]) ).
thf(238,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(1320,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)],[238]) ).
thf(81,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(940,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)],[81]) ).
thf(408,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(1737,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)],[408]) ).
thf(385,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(1681,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)],[385]) ).
thf(692,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(2436,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)],[692]) ).
thf(635,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(2297,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)],[635]) ).
thf(421,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(1769,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(699,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(2453,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)],[699]) ).
thf(549,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(2087,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)],[549]) ).
thf(299,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(1468,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)],[299]) ).
thf(134,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(1069,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)],[134]) ).
thf(789,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(2672,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)],[789]) ).
thf(776,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(2640,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)],[776]) ).
thf(78,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(935,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)],[78]) ).
thf(491,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(1945,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(584,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(2170,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)],[584]) ).
thf(656,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(2351,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(141,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(1088,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)],[141]) ).
thf(191,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(1204,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)],[191]) ).
thf(291,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(1449,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)],[291]) ).
thf(439,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(1812,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)],[439]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( 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(1014,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)],[113]) ).
thf(462,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(1870,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)],[462]) ).
thf(95,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(972,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)],[95]) ).
thf(6145,plain,
$false,
inference(e,[status(thm)],[892,1665,1168,2336,1899,1840,2559,2331,1295,1956,1554,1586,1501,809,2612,1024,1823,1190,2072,1767,1237,846,1315,2499,2427,1083,962,1982,2117,2231,1522,2381,2395,2659,1618,994,2590,878,1533,1041,2363,1200,1750,977,1924,1005,2210,1569,1939,2248,2114,1269,1173,1486,1426,1671,1608,1137,2607,1756,2035,1735,1867,2316,1275,1872,1233,814,2580,945,930,1458,1497,1705,2476,1260,1919,2459,1063,1954,1354,2146,829,1835,2348,1391,1441,1046,1613,1935,1645,1359,1475,2516,1967,1803,2531,1243,1127,2548,2020,841,2136,1904,1623,1254,2328,2667,2339,1907,2217,917,2682,1191,1992,1462,2703,1760,1660,1323,838,1577,1455,2562,2488,949,2571,2356,853,1379,2635,1773,1815,1362,1545,2420,1922,817,2691,902,1319,870,1398,881,1875,1778,1714,2105,2090,1373,1109,2259,2650,834,937,2254,806,2017,2456,2007,2178,2222,1489,1415,2616,1946,1418,2451,2236,1858,1864,2122,1183,1283,1051,821,2058,1377,2281,2190,1447,2371,1526,1351,2002,1201,1600,2154,866,1886,1796,1072,2242,988,2286,2639,2103,1405,1696,2586,1651,942,2204,925,1306,2164,1153,810,1338,1783,2307,2496,1730,2574,1438,1470,1708,2061,2000,1636,2409,1091,2428,1519,1580,862,2133,820,1824,2528,2015,1387,1900,910,957,1223,825,1343,2032,815,1883,1560,2445,2433,2565,1178,1687,2181,2327,2345,974,2464,847,1032,1837,1602,1365,2628,2670,2200,2609,830,1210,1656,1195,2211,1407,2313,1128,2492,1634,2228,2112,1291,1740,1910,842,2653,1106,1541,2577,2694,1096,2631,2537,1118,2268,2245,1350,1592,2300,874,1143,1762,2100,1534,1794,1375,1121,1111,1970,980,2692,1498,2023,2323,1075,1937,1889,970,884,1329,1964,1942,1659,1424,2455,2196,1842,2172,1810,1791,2108,2038,1016,1207,2317,1155,837,1114,1297,1530,1131,1668,1932,2465,984,1799,1984,2482,1720,1979,2272,2140,1393,1525,1776,1263,997,2125,1099,1150,1478,2519,1266,2387,1231,1002,1852,1333,1318,2702,805,2043,1563,1187,1663,2617,888,1732,2634,2749,1434,1857,1846,1054,1286,1035,2368,1026,1167,2645,2189,953,2662,1185,1648,2413,2677,824,1483,1273,1747,856,2602,1631,965,1727,1510,1146,2292,1959,2556,1103,2275,2149,1548,1927,2028,1595,819,904,1833,2727,1916,2048,2225,1615,843,2525,2393,1929,2568,826,1403,1965,1124,1226,1786,2029,1312,1997,2442,2425,2358,1675,1428,2161,1139,1503,1271,1371,1058,1107,1765,1090,1897,919,1464,2474,947,2510,2361,2119,831,2478,2642,1048,1492,2116,1043,1571,1175,2084,2214,2415,1894,2422,1117,1574,1806,1011,1349,2097,990,2257,1589,1722,1144,2378,1690,890,811,1877,1557,2625,816,1162,2446,1381,2461,1820,1688,2025,1080,1339,2605,1029,895,2542,1460,2289,1022,2664,2278,2553,932,1061,1952,2365,959,986,2303,2156,2207,922,1973,2069,2506,912,1171,2075,2418,1396,2439,2401,1699,1213,827,2051,2550,1245,2481,1066,2620,868,2592,1000,2752,2390,1250,1413,1626,2239,1583,1809,2614,1467,2471,927,1134,2333,2597,2054,1948,1758,1166,2503,1684,1277,2234,2449,812,2684,2202,939,1340,968,1181,823,836,1551,2513,1770,1961,2397,2192,1605,1753,1516,1598,1611,2375,1743,1400,1566,2012,1368,2175,2092,1716,2165,1038,840,1235,1830,1085,1579,1336,2468,2656,1711,1300,1452,2688,2219,2128,1538,951,2545,808,1285,1218,2354,907,1543,1802,1702,1221,2145,2320,864,1094,1008,2584,859,1240,2675,2056,1404,2411,2500,1849,1257,1141,1536,2728,1717,2266,876,845,1421,2045,1966,2696,1949,1817,2194,1654,2325,2490,2658,2626,2352,1157,2078,1913,2310,1844,1781,1216,2110,1010,1390,2305,2342,1289,844,1646,1326,1253,2167,2283,896,1639,2251,2406,1508,1101,1745,1854,2130,813,2594,1629,2004,2152,2262,2081,2384,914,2399,2648,1294,2198,2066,1193,1077,1513,899,2623,1994,2019,1614,2009,1861,2680,2183,2095,832,2294,1309,2494,1444,2142,2123,1642,2534,833,1229,818,2522,1248,1480,1725,1280,2385,1678,835,2587,1303,1986,1527,1148,1673,2636,1436,1989,1495,1657,2186,807,1693,1410,2404,1891,828,1473,2040,1165,955,886,1056,1789,1710,1197,1346,2063,839,2241,2159,1827,1976,992,1902,2699,871,2372,2138,2600,1384,2485,2265,1019,1357,2583,822,2507,2539,850,2687,982,1880,1431,1505,2270,1621,1331,803,1320,940,1737,1681,2436,2297,1769,2453,2087,1468,1069,2672,2640,935,1945,2170,2351,1088,1204,1449,1812,1014,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV712-1 : 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
% 0.15/0.42 % Computer : n026.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 14:52:25 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.87/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.31/1.44 % [INFO] Parsing done (419ms).
% 2.31/1.45 % [INFO] Running in sequential loop mode.
% 3.21/1.82 % [INFO] eprover registered as external prover.
% 3.21/1.83 % [INFO] Scanning for conjecture ...
% 3.87/2.08 % [INFO] Found a conjecture (or negated_conjecture) and 803 axioms. Running axiom selection ...
% 5.07/2.34 % [INFO] Axiom selection finished. Selected 801 axioms (removed 2 axioms).
% 6.18/2.68 % [INFO] Problem is propositional (TPTP CNF).
% 6.62/2.71 % [INFO] Type checking passed.
% 6.62/2.72 % [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 ...
% 92.70/38.76 % External prover 'e' found a proof!
% 92.70/38.76 % [INFO] Killing All external provers ...
% 92.70/38.76 % Time passed: 38192ms (effective reasoning time: 37299ms)
% 92.70/38.77 % Axioms used in derivation (801): cls_zero__less__power__eq_1, cls_mult__eq__1__iff_1, cls_root__cancel_0, cls_less__iff__diff__less__0_0, cls_add__0__left_0, cls_xt1_I9_J_0, cls_add__cancel__end_1, cls_power__0_0, cls_mult__numeral__1__right_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, cls_sum__power2__gt__zero__iff_2, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_mult__cancel2_0, cls_less__divide__eq_3, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_divide__eq__eq_3, cls_eq__add__iff2_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_odd__power__less__zero_0, cls_class__ringb_Oadd__r0__iff_1, cls_gb__semiring_Omul__0_0, cls_Suc__inject_0, cls_DERIV__mult__lemma_0, cls_divide__less__0__iff_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_zero__less__divide__iff_5, cls_gb__semiring_Osemiring__rules_I12_J_0, cls_less__divide__eq__number__of1_6, cls_divide__pos__pos_0, clsarity_Int__Oint__Int_Onumber, cls_mult__2__right_0, cls_eq__divide__eq__number__of1_4, cls_add__less__cancel__left_1, cls_mult__right_Ozero_0, cls_gb__semiring_Osemiring__rules_I7_J_0, cls_even__zero__nat_0, cls_divide__eq__eq__number__of_4, cls_mult_Odiff__left_0, cls_mult__less__cancel__right__disj_0, cls_divide__self_0, cls_rel__simps_I43_J_1, cls_power__divides__special_0, cls_sum__squares__eq__zero__iff_0, cls_Suc__n__not__n_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_Bit0__Pls_0, cls_left__minus_0, cls_zero__less__power__eq_5, cls_square__eq__iff_1, cls_minus__zero_0, cls_power__eq__0__iff_1, cls_Lim_Ominus__diff__minus_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, clsarity_Complex__Ocomplex__Int_Onumber, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_comp__arith_I112_J_0, cls_number__of__Bit1_0, cls_mult__is__0_2, cls_gb__semiring_Opwr__pwr_0, cls_divide__numeral__1_0, cls_less__half__sum_0, cls_power__inject__exp_0, cls_class__semiring_Osemiring__rules_I29_J_0, cls_less__antisym_0, cls_divide__less__eq__number__of1_5, clsarity_Int__Oint__Ring__and__Field_Opordered__ring, cls_less__divide__eq__number__of_8, cls_power3__eq__cube_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_half_0, cls_nat__lt__two__imp__zero__or__one_0, cls_linorder__neqE_0, cls_divide__1_0, cls_add__strict__right__mono_0, clsarity_Int__Oint__Orderings_Oorder, cls_power2__less__0_0, cls_even__Suc_0, cls_minus__one__even__power_0, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, clsarity_Int__Oint__OrderedGroup_Omonoid__add, cls_right__distrib__number__of_0, clsarity_fun__Orderings_Oorder, cls_not__sum__squares__lt__zero_0, clsarity_Int__Oint__Ring__and__Field_Osemiring, cls_class__semiring_Osemiring__rules_I20_J_0, cls_half__gt__zero_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_power2__diff_0, cls_zero__less__divide__iff_0, cls_divide__less__eq__number__of1_0, cls_divide__less__eq__number__of_1, cls_gb__semiring_Opwr__Suc_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_add__imp__eq_0, cls_gb__semiring_Osemiring__rules_I3_J_0, cls_less__Suc__eq_2, cls_zero__less__power__eq_4, cls_zero__less__power__nat__eq__number__of_0, cls_minus__diff__eq_0, cls_power__less__zero__eq_1, cls_divide__Numeral1_0, cls_gb__semiring_Osemiring__rules_I28_J_0, cls_number__of__Pls_0, cls_divide__less__eq_4, cls_minus__add__distrib_0, cls_less__divide__eq__number__of_3, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_not__less__eq_1, cls_divide__Numeral0_0, cls_compl__eq__compl__iff_0, cls_left__distrib__number__of_0, cls_minus__divide__right_0, clsarity_nat__Orderings_Olinorder, cls_eq__divide__eq__number__of_4, cls_class__ring_Osub__add_0, cls_comm__monoid__add_Omult__1__right_0, cls_minus__minus_0, cls_power__one_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_divide__less__eq_5, cls_neg__less__iff__less_1, cls_power__0__left__number__of_0, cls_add__cancel__21_1, cls_left__diff__distrib__number__of_0, cls_divide__less__eq__number__of1_6, cls_gb__semiring_Osemiring__rules_I13_J_0, cls_nat__power__eq__Suc__0__iff_1, cls_divide__eq__eq_0, cls_class__ringb_Onoteq__reduce_0, cls_rel__simps_I49_J_0, cls_power__gt1_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, cls_zero__less__power__eq__number__of_1, cls_Suc__mult__cancel1_0, cls_eq__divide__eq__number__of_1, cls_zero__eq__power2_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_less__minus__iff_0, cls_power__less__imp__less__exp_0, cls_gr0I_0, cls_mult__minus1_0, cls_mult__less__cancel2_1, cls_mult__less__cancel__right__disj_3, cls_eq__add__iff1_0, clsarity_Int__Oint__Ring__and__Field_Oring__1, cls_power__less__zero__eq__number__of_1, cls_Suc__double__inj__on_0, clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors, cls_even__product__nat_1, cls_mult__less__cancel1_0, cls_minus__unique_0, cls_COMBB__def_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_even__power__nat_1, cls_less__divide__eq_4, cls_mult__eq__0__iff_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_zero__power2_0, clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add, cls_divide__strict__left__mono_0, cls_gb__semiring_Oadd__c_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, clsarity_nat__Ring__and__Field_Osemiring__0, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1, cls_divide__less__eq__number__of_6, cls_power__m1__odd_0, cls_divide__eq__eq_4, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_one__add__one__is__two_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict, cls_double__add__less__zero__iff__single__less__zero_0, cls_less__divide__eq__number__of1_2, cls_nat__number__of__Pls_0, cls_gb__semiring_Omul__c_0, cls_n__less__n__mult__m_0, cls_less__iff__diff__less__0_1, cls_nat__less__cases_0, cls_eq__divide__eq_4, cls_nat__mult__eq__cancel1_0, cls_ab__left__minus_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_rel__simps_I38_J_1, cls_field__power__not__zero_0, cls_neg__equal__iff__equal_0, cls_frac__eq__eq_0, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_less__add__iff2_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_mult_Ozero__left_0, cls_divide__neg__neg_0, cls_mult__2_0, cls_power__minus1__even_0, cls_power__eq__0__iff__number__of_2, cls_less__divide__eq__number__of1_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_eq__number__of_0, cls_mult_Ozero__right_0, cls_divide__strict__left__mono__neg_0, cls_mult__strict__right__mono_0, cls_class__semiring_Omul__c_0, cls_Suc__mult__less__cancel1_0, cls_mult_Oadd__left_0, cls_mult__pos__neg_0, cls_zero__less__power__eq__number__of_4, cls_nat__0__less__mult__iff_0, cls_divide__eq__eq__number__of1_0, clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, cls_right__minus__eq_0, cls_mult__eq__1__iff_0, cls_divide__less__eq__number__of1_8, cls_gb__semiring_Omul__d_0, cls_sum__power2__gt__zero__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_add__cancel__end_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_i_0, cls_gb__semiring_Osemiring__rules_I16_J_0, cls_minus__less__iff_1, cls_gb__semiring_Osemiring__rules_I14_J_0, cls_eq__divide__eq__number__of1_3, cls_mult__right_Oadd_0, cls_linorder__neqE__nat_0, cls_minus__add__cancel_0, cls_power__Suc2_0, cls_power__one__over_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_less__divide__eq_7, cls_minus__one__odd__power_0, cls_xt1_I10_J_0, clsarity_Int__Oint__Int_Oring__char__0, cls_comm__ring__1__class_Opower__minus__even_0, cls_add__less__cancel__right_1, cls_root0_0, cls_add__divide__distrib_0, cls_not__less__iff__gr__or__eq_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_no__zero__divisors_0, cls_mult__frac__num_0, cls_numeral__1__eq__1_0, cls_power__gt1__lemma_0, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_divide__neg__pos_0, cls_mult__is__0_1, cls_less__divide__eq__number__of_7, cls_mult__less__cancel2_2, cls_even__Suc_1, cls_rel__simps_I39_J_0, cls_divide__less__eq_0, cls_zero__less__power__eq__number__of_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_mult__frac__frac_0, cls_zero__less__power__nat__eq__number__of_2, cls_class__semiring_Osemiring__rules_I2_J_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semidom, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_gb__semiring_Osemiring__rules_I9_J_0, cls_divide__less__eq__number__of_0, cls_less__divide__eq_2, cls_power__strict__increasing_0, cls_not__sum__power2__lt__zero_0, cls_class__semiring_Osemiring__rules_I37_J_0, cls_combine__common__factor_0, clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult, cls_zero__less__divide__iff_1, cls_divide__less__eq__number__of1_2, cls_ATP__Linkup_OCOMBC__def_0, cls_mult__1__right_0, cls_gb__semiring_Omul__1_0, cls_zero__less__power__nat__eq_1, cls_divide__eq__eq__number__of_3, cls_add__strict__left__mono_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_power__0__Suc_0, cls_sum__power2__eq__zero__iff_0, cls_nat__zero__less__power__iff_0, cls_neg__one__even__power_0, cls_mult__neg__pos_0, cls_mult__left_Odiff_0, cls_less__add__iff1_0, cls_even__nat__equiv__def2_1, cls_divide__eq__eq__number__of1_3, cls_Suc__neq__Zero_0, cls_gb__semiring_Osemiring__rules_I25_J_0, cls_diff__minus_0, clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors, cls_class__ringb_Onoteq__reduce_1, cls_root__cancel1_0, cls_power__mult_0, cls_rel__simps_I38_J_0, cls_gb__semiring_Osemiring__rules_I21_J_0, cls_comp__arith_I115_J_0, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add, cls_mult__pos__neg2_0, cls_divide__less__eq__number__of1_7, cls_power__eq__0__iff_2, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__less__cancel__left__disj_0, cls_class__semiring_Oadd__a_0, cls_minus__mult__commute_0, cls_zero__eq__power2_1, cls_class__semiring_Osemiring__rules_I19_J_0, cls_gb__semiring_Osemiring__rules_I5_J_0, cls_power__0__left__number__of_1, cls_add__right__cancel_0, cls_mult_Odiff__right_0, cls_less__add__iff2_1, cls_less__divide__eq__number__of1_3, cls_eq__divide__eq_3, cls_mult__less__cancel1_1, cls_less__divide__eq__number__of_4, clsarity_Complex__Ocomplex__Int_Oring__char__0, 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% 92.70/38.77 % No. of inferences in proof: 1627
% 92.70/38.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38192 ms resp. 37299 ms w/o parsing
% 94.29/39.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 94.29/39.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------