TSTP Solution File: SWV632-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV632-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:17:38 EDT 2023
% Result : Unsatisfiable 85.41s 18.94s
% Output : Refutation 86.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1582
% Syntax : Number of formulae : 3065 ( 525 unt; 100 typ; 0 def)
% Number of atoms : 8863 (1816 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 47222 (5370 ~;5898 |; 0 &;35954 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 100 usr; 10 con; 0-3 aty)
% Number of variables : 7512 ( 0 ^;7512 !; 0 ?;7512 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_FFT__Mirabelle_Oroot_type,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
thf(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
thf(c_Int_OPls_type,type,
c_Int_OPls: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(v_m_type,type,
v_m: $i ).
thf(v_i_type,type,
v_i: $i ).
thf(v_j_type,type,
v_j: $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(class_OrderedGroup_Oordered__ab__group__add_type,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(class_OrderedGroup_Opordered__ab__group__add__abs_type,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
thf(c_HOL_Oabs__class_Oabs_type,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Olordered__ring_type,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Oabs__if_type,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_Divides_Oring__div_type,type,
class_Divides_Oring__div: $i > $o ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring__abs_type,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add__abs_type,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_type,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(class_Int_Onumber_type,type,
class_Int_Onumber: $i > $o ).
thf(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Parity_Oeven__odd__class_Oeven_type,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_type,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(c_Int_Oiszero_type,type,
c_Int_Oiszero: $i > $i > $o ).
thf(class_Ring__and__Field_Oring__1_type,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_Int_OMin_type,type,
c_Int_OMin: $i ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_type,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Odvd_type,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_type,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_type,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_RealVector_Oreal__field_type,type,
class_RealVector_Oreal__field: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Omult__mono_type,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Complex_Oii_type,type,
c_Complex_Oii: $i ).
thf(c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1_type,type,
c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1: $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(2163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(1665,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(2094,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1030,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(3883,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(1120,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(4094,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(1478,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_4) ).
thf(4899,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(597,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(2876,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(819,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(3397,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(898,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(3581,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(221,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(1982,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(461,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(2544,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(2331,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(892,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(3566,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(30,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).
thf(1549,plain,
class_OrderedGroup_Olordered__ab__group__add__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(720,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
thf(3172,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1025,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
thf(3873,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1162,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).
thf(4188,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(47,axiom,
class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
thf(1586,plain,
class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1168,axiom,
! [A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__even__iff__2__dvd_0) ).
thf(4201,plain,
! [A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1328,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(4560,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(1062,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(3962,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(354,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(2295,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1332,axiom,
class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
thf(4571,plain,
class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(1280,axiom,
! [A: $i] :
( ( c_Int_OBit0 @ A )
!= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I45_J_0) ).
thf(4450,plain,
! [A: $i] :
( ( c_Int_OBit0 @ A )
!= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1287,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_2) ).
thf(4464,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(649,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(3008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1444,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit1_0) ).
thf(4824,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(2131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1482,axiom,
class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(4909,plain,
class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(2072,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1195,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ B ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).
thf(4262,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ B ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(933,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(3661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_2) ).
thf(1767,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(820,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(3399,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(342,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ E @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ E @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
thf(2263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ E @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ E @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1049,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(3930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(935,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(3666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1089,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(4022,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(1729,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(836,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(3434,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(718,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
thf(3167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
thf(2921,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(1208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_2) ).
thf(4290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(855,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(3477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(949,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(3698,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(1069,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(3979,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(1021,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(3863,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1007,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
!= ( c_Power_Opower__class_Opower @ D @ ( c_Suc @ C ) @ A ) )
| ( B = D )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(3830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
!= ( c_Power_Opower__class_Opower @ D @ ( c_Suc @ C ) @ A ) )
| ( B = D )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(1469,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1__right_0) ).
thf(4877,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(1818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(2250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(2077,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(1750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1179,axiom,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(4226,plain,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1232,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__2__eq__Suc_H_0) ).
thf(4339,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(1113,axiom,
! [A: $i] :
( ( c_Int_Onumber__class_Onumber__of @ A @ tc_Int_Oint )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__is__id_0) ).
thf(4075,plain,
! [A: $i] :
( ( c_Int_Onumber__class_Onumber__of @ A @ tc_Int_Oint )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(397,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ A ) @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__plus__one__div__two_0) ).
thf(2395,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ A ) @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1256,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(4391,plain,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(1041,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
thf(3912,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(694,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
thf(3108,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).
thf(1591,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1174,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(4215,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1408,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(4747,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(942,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(3681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(1074,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).
thf(3990,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1095,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Otimes__class_Otimes @ E @ F @ A ) @ A ) @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(4037,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Otimes__class_Otimes @ E @ F @ A ) @ A ) @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(2512,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(679,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(3072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__Suc_0) ).
thf(1924,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(2117,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber @ A )
| ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0__number__of_0) ).
thf(2940,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber @ A )
| ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(274,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(2104,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ A @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).
thf(2808,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ A @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1038,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).
thf(3905,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
thf(2644,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1308,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
thf(4515,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(439,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
thf(2495,plain,
class_Ring__and__Field_Oordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(745,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
thf(3230,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(2381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(1808,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(2659,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(768,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).
thf(3285,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(846,axiom,
class_Ring__and__Field_Omult__mono @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
thf(3460,plain,
class_Ring__and__Field_Omult__mono @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1435,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__0__le__power__imp__0__le_0) ).
thf(4807,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(1388,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(4697,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(1061,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(3959,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(516,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(2671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(27,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).
thf(1544,plain,
class_OrderedGroup_Opordered__ab__group__add__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1040,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(3910,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1346,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(4603,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(651,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
thf(3012,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(1971,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1351,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(4614,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(2854,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).
thf(1692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
thf(4408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(2,axiom,
class_OrderedGroup_Oordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
thf(1486,plain,
class_OrderedGroup_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1316,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).
thf(4532,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(928,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(3649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(665,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).
thf(3044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(985,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(3781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).
thf(2146,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(764,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(3276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).
thf(2195,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(100,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(1705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(135,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).
thf(1788,plain,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(3217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(991,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(3794,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(838,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
thf(3439,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(668,axiom,
class_Ring__and__Field_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
thf(3049,plain,
class_Ring__and__Field_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(1404,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(4739,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(2035,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(805,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
thf(3367,plain,
class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(804,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(3365,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1466,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_Suc @ B ) ) ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ A @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__mod__add3_0) ).
thf(4870,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_Suc @ B ) ) ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ A @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(545,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(2740,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(170,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(1867,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1177,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs__number__of_0) ).
thf(4220,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1314,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_0) ).
thf(4528,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(2184,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(721,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(3175,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(2448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(2933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(1361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).
thf(4638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1872,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1367,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
thf(4650,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(2627,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(1919,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(755,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(3253,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(2459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(827,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(3414,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(699,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
thf(3121,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(1210,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(4294,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(1274,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ ( c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1 @ A ) @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__mult__two__ex_0) ).
thf(4435,plain,
! [A: $i] :
( ( A
= ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ ( c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1 @ A ) @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(896,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(3577,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(2042,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(807,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(3370,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(1099,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(4047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(797,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(3350,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).
thf(1914,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(1166,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(4198,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(707,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(3140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(998,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(3809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(1190,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(4249,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1252,axiom,
class_Ring__and__Field_Odvd @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(4386,plain,
class_Ring__and__Field_Odvd @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(2216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(1234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_1) ).
thf(4343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(921,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_0) ).
thf(3634,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__le__imp__le_0) ).
thf(4142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(554,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__0_0) ).
thf(2763,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1042,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(3915,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
thf(1782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).
thf(2227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(1576,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(753,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half_0) ).
thf(3249,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1246,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).
thf(4371,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(1197,axiom,
! [A: $i] :
( ( ( c_Int_OBit1 @ A )
!= c_Int_OMin )
| ( A = c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I47_J_0) ).
thf(4266,plain,
! [A: $i] :
( ( ( c_Int_OBit1 @ A )
!= c_Int_OMin )
| ( A = c_Int_OMin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(870,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(3513,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1381,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
thf(4679,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(779,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(3308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1056,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(3947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(73,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Obot__least_0) ).
thf(1645,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(766,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_3) ).
thf(3281,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(2400,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).
thf(2067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(1529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).
thf(1967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1224,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(4322,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(2819,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__less__dividend_0) ).
thf(1803,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(288,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(2136,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(17,axiom,
class_Ring__and__Field_Opordered__ring__abs @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).
thf(1518,plain,
class_Ring__and__Field_Opordered__ring__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).
thf(2531,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(2405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(3221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
thf(2603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(666,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
thf(3046,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(2269,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(895,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(3574,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1003,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(3821,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(686,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
thf(3089,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
thf(1832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1331,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_5) ).
thf(4568,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(530,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__pos__nat_0) ).
thf(2703,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(1033,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).
thf(3891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1360,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(4637,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(752,axiom,
class_Int_Onumber__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(3248,plain,
class_Int_Onumber__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_0) ).
thf(4238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(1320,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__one__even__power_0) ).
thf(4539,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(839,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(3442,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1052,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
thf(3938,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(659,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).
thf(3029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1463,axiom,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_Int_Oint )
= ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transfer__int__nat__numerals_I3_J_0) ).
thf(4866,plain,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_Int_Oint )
= ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
thf(1792,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(926,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(3644,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).
thf(2735,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(1329,axiom,
! [A: $i] :
( ( c_Int_OPls
!= ( c_Int_OBit0 @ A ) )
| ( c_Int_OPls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).
thf(4563,plain,
! [A: $i] :
( ( c_Int_OPls
!= ( c_Int_OBit0 @ A ) )
| ( c_Int_OPls = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(1268,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(4422,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(2698,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(1660,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(4070,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(697,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero_0) ).
thf(3116,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(1147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
!= ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) )
| ( B = C )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__imp__eq_0) ).
thf(4151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
!= ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) )
| ( B = C )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1415,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(4761,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(3061,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
thf(1907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(442,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(2501,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1369,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(4654,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(913,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(3617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).
thf(2444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
thf(1860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1511,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_2) ).
thf(2274,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(1423,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
thf(4778,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(983,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
thf(3776,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(2682,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ D @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(4130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ D @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(883,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(3542,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1201,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
thf(4275,plain,
class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(1417,axiom,
! [A: $i] : ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__mult__two__ex_1) ).
thf(4766,plain,
! [A: $i] : ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(1271,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(4428,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( B
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).
thf(2745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( B
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(956,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(3713,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).
thf(2356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(1922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(690,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
thf(3099,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(872,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(3517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1352,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).
thf(4617,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1221,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(4317,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(1058,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(3951,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1009,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
thf(3835,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1255,axiom,
class_Ring__and__Field_Omult__mono @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(4390,plain,
class_Ring__and__Field_Omult__mono @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(1420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(4771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
thf(1847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1545,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(407,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(2420,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1011,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(3840,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(813,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(3385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
thf(2857,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(1238,axiom,
( ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__Pls_0) ).
thf(4353,plain,
( ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(1461,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(4862,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
thf(2169,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(923,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(3638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(1159,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__eq__power2_0) ).
thf(4179,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1374,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
thf(4664,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(1299,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(4492,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(1354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(4622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(499,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(2635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(618,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(2929,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1379,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).
thf(4675,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(852,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
thf(3470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(781,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
thf(3312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1324,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(4551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(1037,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
thf(3902,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(964,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
thf(3734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1245,axiom,
! [A: $i] :
( ( ( c_Int_OBit0 @ A )
!= c_Int_OPls )
| ( A = c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I44_J_0) ).
thf(4368,plain,
! [A: $i] :
( ( ( c_Int_OBit0 @ A )
!= c_Int_OPls )
| ( A = c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(652,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(3014,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1141,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(4141,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(1196,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(4265,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(1773,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_1) ).
thf(4383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(147,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).
thf(1815,plain,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1284,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(4460,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(641,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(2989,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).
thf(1963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1429,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
thf(4793,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1215,axiom,
! [A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__even__iff__2__dvd_1) ).
thf(4302,plain,
! [A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1022,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(3866,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1192,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).
thf(4253,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(761,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(3268,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1082,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
thf(4008,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(757,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__less_0) ).
thf(3258,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1413,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power2_0) ).
thf(4756,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(579,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(2829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(785,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(3322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(875,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(3524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(4583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(731,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
thf(3199,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(1459,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus1__even_0) ).
thf(4857,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(2451,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(876,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(3527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(1682,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1326,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(4556,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(1273,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__gr__0_1) ).
thf(4432,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(423,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(2456,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(2178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1264,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).
thf(4411,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(1170,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(4205,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(2237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
thf(2616,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(205,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(1946,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1480,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_1) ).
thf(4903,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(2105,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(680,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(3075,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(1111,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(4072,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1087,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
thf(4018,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(817,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(3393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(1911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1282,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(4454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(1345,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__even__div2_0) ).
thf(4600,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
thf(2782,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(603,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus1__divide_0) ).
thf(2893,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(1632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
thf(2469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1079,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(4001,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(937,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(3670,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(1402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_3) ).
thf(4733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__even__power_0) ).
thf(1858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1145,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(4147,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1439,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(4815,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(1399,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(4724,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(915,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
thf(3621,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(616,axiom,
! [A: $i] :
( A
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(2925,plain,
! [A: $i] :
( A
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(1066,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(3973,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(893,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(3569,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(1677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(459,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(2540,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(466,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(2555,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(775,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).
thf(3300,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1045,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).
thf(3923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1131,axiom,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__numeral__1__eq__1_0) ).
thf(4115,plain,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(2335,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(559,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
thf(2777,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(712,axiom,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) @ tc_nat ) )
= A )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__div__two__times__two__plus__one_0) ).
thf(3152,plain,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) @ tc_nat ) )
= A )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(981,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(3771,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1151,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
thf(4162,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(1072,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).
thf(3986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1453,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__2__cases_0) ).
thf(4842,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(955,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_1) ).
thf(3712,plain,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(2483,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(662,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
thf(3036,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1364,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__power__less__zero_0) ).
thf(4643,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(569,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_2) ).
thf(2804,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(1474,axiom,
! [A: $i] :
( ( c_Int_OMin
!= ( c_Int_OBit1 @ A ) )
| ( c_Int_OMin = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_0) ).
thf(4892,plain,
! [A: $i] :
( ( c_Int_OMin
!= ( c_Int_OBit1 @ A ) )
| ( c_Int_OMin = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(1356,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
thf(4628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
thf(2718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(810,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_3) ).
thf(3378,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(815,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
thf(3389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(445,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(2508,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__even__power_H_0) ).
thf(4718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(1410,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(4751,plain,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).
thf(2367,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(415,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(2437,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(2618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(966,axiom,
! [A: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ A @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def2_1) ).
thf(3739,plain,
! [A: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ A @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(2281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
thf(1896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(830,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).
thf(3421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(944,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).
thf(3685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).
thf(1886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1304,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral1__eq1__nat_0) ).
thf(4504,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(1243,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
thf(4364,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(2424,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(21,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1526,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1217,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I37_J_0) ).
thf(4307,plain,
c_Int_OPls != c_Int_OMin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(940,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(3676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(974,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(3756,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1318,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
thf(4536,plain,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(750,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(3243,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Oabs__class_Oabs @ C @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
thf(2286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Oabs__class_Oabs @ C @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(501,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
thf(2639,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(908,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ C @ tc_nat ) @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult2__eq_0) ).
thf(3606,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ C @ tc_nat ) @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(736,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
thf(3211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(2392,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(2154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
thf(1521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
thf(1696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(726,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).
thf(3184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1292,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
thf(4475,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(869,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(3510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1108,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
thf(4065,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(1604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1347,axiom,
( c_Int_OMin
= ( c_Int_OBit1 @ c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_1) ).
thf(4604,plain,
( c_Int_OMin
= ( c_Int_OBit1 @ c_Int_OMin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(1018,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
thf(3857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1175,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__ring__1__class_Opower__minus__even_0) ).
thf(4216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oabs__class_Oabs @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
thf(2204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oabs__class_Oabs @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(1340,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_2) ).
thf(4589,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
thf(2574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(727,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(3186,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).
thf(1708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(502,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(2641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(842,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_0) ).
thf(3450,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(1167,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A ) @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_1) ).
thf(4199,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A ) @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1071,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(3984,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(719,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(3169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(504,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(2646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1016,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(3852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1315,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(4531,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(878,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
thf(3531,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(2364,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1076,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(3995,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).
thf(2047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(783,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).
thf(3318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(2232,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(3054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
thf(2083,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(1736,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1124,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat )
= ( c_Suc @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__2__eq__Suc_0) ).
thf(4100,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat )
= ( c_Suc @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(440,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
thf(2496,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(2621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
thf(4059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(1868,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(2061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(886,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
thf(3550,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1155,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_Suc @ B ) ) ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ A @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__Suc__eq__div__add3_0) ).
thf(4172,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_Suc @ B ) ) ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ A @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(229,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ A ) @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__plus__one__div__two_0) ).
thf(2000,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ A ) @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(1636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(2589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_3) ).
thf(2705,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1288,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult2__eq_0) ).
thf(4466,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(1086,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(4016,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(907,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(3603,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1119,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
thf(4091,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(1311,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(4521,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(1449,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(4836,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(2441,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(517,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
thf(2673,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(1900,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(1723,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(758,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(3261,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(1394,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
thf(4712,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(485,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(2601,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1006,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(3827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(1519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__odd__power_1) ).
thf(2596,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(1259,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(4397,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(1349,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_4) ).
thf(4609,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(2133,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(746,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(3233,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(622,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__neg_0) ).
thf(2937,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1279,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(4449,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(704,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).
thf(3134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1205,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Suc @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__Suc__Suc_0) ).
thf(4284,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Suc @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(295,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(2150,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(2032,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(1442,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(4821,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(1000,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
thf(3814,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(640,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(2986,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1373,axiom,
! [B: $i,A: $i] :
( ( c_Int_OBit0 @ A )
!= ( c_Int_OBit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).
thf(4661,plain,
! [B: $i,A: $i] :
( ( c_Int_OBit0 @ A )
!= ( c_Int_OBit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(934,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(3664,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(792,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).
thf(3339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(2015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(769,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(3286,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1883,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
thf(1560,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(2958,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(822,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(3403,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).
thf(1951,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber @ A )
| ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0__number__of_1) ).
thf(1888,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber @ A )
| ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1422,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).
thf(4776,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ D @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__lemma_0) ).
thf(2200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ D @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).
thf(1656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
thf(2327,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(961,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_2) ).
thf(3727,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(508,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ A @ tc_Int_Oint )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ B @ tc_Int_Oint ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_int__int__eq_0) ).
thf(2653,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ A @ tc_Int_Oint )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ B @ tc_Int_Oint ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(762,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).
thf(3271,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1211,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_0) ).
thf(4295,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(2464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(552,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(2758,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(596,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus__one_0) ).
thf(2873,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
thf(2433,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(431,axiom,
c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
thf(2477,plain,
c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(706,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
thf(3137,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(864,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(3499,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(3065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(971,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(3750,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(796,axiom,
class_Ring__and__Field_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
thf(3349,plain,
class_Ring__and__Field_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1034,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(3894,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
thf(1624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1261,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).
thf(4402,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(880,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(3535,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(157,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).
thf(1836,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(2181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(669,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(3050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(2345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(2313,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(977,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(3763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(2492,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1126,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_2) ).
thf(4104,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
thf(1634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1285,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
thf(4461,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(2112,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(4080,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(661,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(3033,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
thf(1740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(40,axiom,
class_Ring__and__Field_Opordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
thf(1573,plain,
class_Ring__and__Field_Opordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(993,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
thf(3799,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(903,axiom,
! [A: $i] : ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def2_1) ).
thf(3595,plain,
! [A: $i] : ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(840,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).
thf(3445,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1091,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(4027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(1983,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(625,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(2946,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1189,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(4248,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).
thf(2709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(691,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ F @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ F @ A ) @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
thf(3102,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ F @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ F @ A ) @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).
thf(2631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(1084,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
thf(4012,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1053,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
thf(3941,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(646,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).
thf(3001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1064,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
thf(3968,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(1134,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
thf(4123,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(692,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(3105,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(850,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(3467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).
thf(2300,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(2498,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(26,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1541,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(2157,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(584,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(2840,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(2115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(857,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ A @ C @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ A @ C @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add1__eq_0) ).
thf(3482,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ A @ C @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ A @ C @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(1762,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
thf(2100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(2377,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1376,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).
thf(4668,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(568,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(2801,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(138,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
thf(1794,plain,
class_Ring__and__Field_Opordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(1953,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1307,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__exhaust__less__4_0) ).
thf(4512,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(1128,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).
thf(4108,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(635,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(2973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1296,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ A @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__self__div__2_0) ).
thf(4486,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ A @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(1428,axiom,
! [B: $i,A: $i] :
( ( ( c_Int_OBit0 @ A )
!= ( c_Int_OBit0 @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).
thf(4789,plain,
! [B: $i,A: $i] :
( ( ( c_Int_OBit0 @ A )
!= ( c_Int_OBit0 @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).
thf(1856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1359,axiom,
class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
thf(4636,plain,
class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(48,axiom,
class_Ring__and__Field_Oordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
thf(1587,plain,
class_Ring__and__Field_Oordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(4525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(1386,axiom,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__Suc__0_0) ).
thf(4693,plain,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(1454,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(4845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(539,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
!= B )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(2724,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
!= B )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
thf(1719,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1180,axiom,
! [A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_0) ).
thf(4227,plain,
! [A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(920,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(3632,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1121,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(4095,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(969,axiom,
class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
thf(3746,plain,
class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1451,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(4840,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(1471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
thf(4883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(734,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(3205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(1176,axiom,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
thf(4219,plain,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(3087,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(654,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(3018,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1477,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(4898,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(1380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(4676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(708,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(3143,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(1460,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_2) ).
thf(4860,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(1202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__less__imp__less_0) ).
thf(4276,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(1322,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(4545,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(332,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(2240,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(4191,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(378,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(2349,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(2108,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).
thf(2551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1223,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
thf(4320,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
thf(2798,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(1229,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).
thf(4333,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1059,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).
thf(3954,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(4049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(1310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(4518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(1214,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(4301,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(787,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(3326,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).
thf(2323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(723,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
thf(3179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(824,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ D @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono__even_0) ).
thf(3407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ D @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(468,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_2) ).
thf(2561,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(688,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
thf(3094,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1153,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__m1__even_0) ).
thf(4167,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(2868,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1254,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(4389,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(904,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(3596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1220,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(4315,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(650,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(3010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
thf(1937,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(2172,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(1366,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__div__eq__add3__div__number__of_0) ).
thf(4648,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(1103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__add_0) ).
thf(4054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(833,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(3428,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).
thf(4444,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(514,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(2666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(888,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(3555,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1283,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(4457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
thf(2649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(2978,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(429,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).
thf(2472,plain,
! [A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(772,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
thf(3294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(1403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(4736,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(117,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1744,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1433,axiom,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(4804,plain,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).
thf(2519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(968,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(3743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(2851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(1932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1002,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(3819,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(882,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(3540,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).
thf(2566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1133,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(4120,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(1874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1194,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus1__odd_0) ).
thf(4259,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(739,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(3215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(951,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).
thf(3703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(2968,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(443,axiom,
! [A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ A ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_1) ).
thf(2504,plain,
! [A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ A ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).
thf(1776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(911,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).
thf(3611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(931,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(3656,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(859,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(3486,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(930,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(3654,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
thf(1588,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(457,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
thf(2536,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(701,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(3126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(988,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).
thf(3787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(582,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(2836,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(436,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).
thf(2487,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(484,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(2598,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).
thf(3059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(799,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
thf(3354,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(2900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_0) ).
thf(1668,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(1974,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1236,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Pls_0) ).
thf(4347,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).
thf(1852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(573,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_1) ).
thf(2813,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(976,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(3760,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(825,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).
thf(3409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(947,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(3692,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
thf(2052,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
thf(1599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1479,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(4902,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).
thf(1715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(790,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
thf(3333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(220,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(1979,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
!= ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(3005,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
!= ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1266,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(4416,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(1044,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(3920,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(2272,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).
thf(2140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_0) ).
thf(2756,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(716,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(3162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(732,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(3201,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(1178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_0) ).
thf(4223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(122,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(1759,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(710,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(3147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(1317,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(4535,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1146,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(4148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(563,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
thf(2788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(995,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_1) ).
thf(3802,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1355,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__power2_0) ).
thf(4625,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(778,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
thf(3306,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(2748,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(2402,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(868,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(3508,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(2529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(462,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
thf(2546,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(891,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(3563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(765,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
thf(3279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1173,axiom,
! [B: $i,A: $i] :
( ( c_Int_OBit1 @ A )
!= ( c_Int_OBit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I50_J_0) ).
thf(4212,plain,
! [B: $i,A: $i] :
( ( c_Int_OBit1 @ A )
!= ( c_Int_OBit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1473,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(4889,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(900,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).
thf(3587,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1078,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(3999,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(631,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(2963,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1481,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
thf(4906,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(611,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(2915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(2408,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(2793,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(728,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(3190,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(1515,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_5) ).
thf(2221,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(311,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(2189,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono__odd_0) ).
thf(1616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1080,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(4004,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(227,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
thf(1996,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(939,axiom,
class_OrderedGroup_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
thf(3675,plain,
class_OrderedGroup_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(1732,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1333,axiom,
( ( c_Int_OBit1 @ c_Int_OMin )
= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit1__Min_0) ).
thf(4572,plain,
( ( c_Int_OBit1 @ c_Int_OMin )
= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(609,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(2909,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(997,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(3807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(953,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(3707,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(353,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(2292,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(1698,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1024,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
thf(3871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(478,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(2585,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(4594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(1468,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__gr__0_0) ).
thf(4874,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(1927,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(770,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
thf(3289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1198,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(4269,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(1298,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).
thf(4489,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
thf(2121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
thf(2235,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(2144,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(621,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(2936,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(541,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__one__even__power_0) ).
thf(2729,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(1648,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(404,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_1) ).
thf(2413,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(2677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(2176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(1392,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(4708,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(1467,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_0) ).
thf(4872,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(861,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(3491,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1,negated_conjecture,
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ v_m @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ v_i @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ v_j @ tc_nat ) @ tc_nat ) @ tc_Complex_Ocomplex )
!= ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ v_m ) @ ( c_HOL_Otimes__class_Otimes @ v_i @ v_j @ tc_nat ) @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1483,plain,
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ v_m @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ v_i @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ v_j @ tc_nat ) @ tc_nat ) @ tc_Complex_Ocomplex )
!= ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ v_m ) @ ( c_HOL_Otimes__class_Otimes @ v_i @ v_j @ tc_nat ) @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
thf(2570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1193,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).
thf(4256,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(1275,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power2_1) ).
thf(4438,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(809,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(3375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1032,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Min_0) ).
thf(3888,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1335,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
thf(4577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(990,axiom,
! [A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_1) ).
thf(3792,plain,
! [A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1241,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__abs_0) ).
thf(4359,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(695,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(3111,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(763,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
thf(3274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
thf(2524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(1281,axiom,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(4453,plain,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(794,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(3343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(714,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).
thf(3158,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(340,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
thf(2260,plain,
class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1426,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(4786,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(1143,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(4144,plain,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(814,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(3387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(866,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(3504,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1036,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).
thf(3900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(1965,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(2695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(578,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(2827,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(737,axiom,
class_Divides_Osemiring__div @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).
thf(3213,plain,
class_Divides_Osemiring__div @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(967,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(3741,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(885,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
thf(3547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1233,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(4341,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(678,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
thf(3070,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).
thf(2727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(979,axiom,
class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
thf(3768,plain,
class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(1916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(922,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(3636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1046,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(3925,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(1784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1300,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(4494,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(4077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(999,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arith__simps_I31_J_0) ).
thf(3811,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(564,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(2791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(749,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
thf(3240,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(910,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_0) ).
thf(3609,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(587,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).
thf(2849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(2657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_1) ).
thf(4159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(853,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(3472,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(965,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(3736,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(975,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).
thf(3758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(198,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1929,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1055,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(3945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(767,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).
thf(3283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(760,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(3266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(2514,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).
thf(2568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1093,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(4032,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_2) ).
thf(4709,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(1535,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(2806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(1795,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(901,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(3590,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(2398,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1226,axiom,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ A ) @ A @ tc_Complex_Ocomplex )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
thf(4328,plain,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ A ) @ A @ tc_Complex_Ocomplex )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(536,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__number__of__Min_0) ).
thf(2716,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1250,axiom,
( ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I115_J_0) ).
thf(4381,plain,
( ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(1023,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
thf(3868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1350,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(4612,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(1191,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Pls_0) ).
thf(4251,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(1319,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
thf(4537,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(982,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
thf(3773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(927,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ B @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(3646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ B @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1443,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2_0) ).
thf(4822,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(1997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(700,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(3123,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(986,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(3783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(828,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(3416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(777,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
thf(3304,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(687,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(3091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(776,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
thf(3302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(1187,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(4245,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(1675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(656,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(3023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1327,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(4558,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(2193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(1786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(698,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).
thf(3118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1136,axiom,
! [A: $i] :
( c_Int_OMin
!= ( c_Int_OBit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I42_J_0) ).
thf(4127,plain,
! [A: $i] :
( c_Int_OMin
!= ( c_Int_OBit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ B @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
thf(2029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ B @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1122,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(4096,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(1430,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(4796,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(2891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(359,axiom,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ B @ A @ tc_nat ) ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div__lemma_2) ).
thf(2308,plain,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ B @ A @ tc_nat ) ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(681,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(3077,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(1365,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_1) ).
thf(4645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(948,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(3695,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(789,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).
thf(3330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(2738,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(735,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(3208,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(1865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(2753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(837,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(3436,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(914,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).
thf(3619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(897,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(3579,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1458,axiom,
! [A: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
thf(4854,plain,
! [A: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(1362,axiom,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(4640,plain,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(2358,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
thf(2148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(958,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_4) ).
thf(3719,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(446,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(2510,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(941,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(3678,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(451,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).
thf(2521,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(458,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__1_0) ).
thf(2538,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
thf(2415,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(963,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(3732,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(4586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).
thf(2065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_1) ).
thf(2079,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(383,axiom,
class_Ring__and__Field_Osemiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
thf(2361,plain,
class_Ring__and__Field_Osemiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(2721,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).
thf(2119,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(798,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
thf(3352,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1231,axiom,
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I113_J_0) ).
thf(4337,plain,
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(2679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1302,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1_0) ).
thf(4498,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(2478,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
thf(3251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(713,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
thf(3155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).
thf(2229,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(748,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).
thf(3238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(2214,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(393,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(2383,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(2624,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(2637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(408,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(2422,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1060,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
thf(3957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(558,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(2774,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(943,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).
thf(3683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
thf(1524,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1446,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).
thf(4828,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(871,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ C ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
thf(3515,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ C ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(984,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(3779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(2906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(829,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(3419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
thf(4699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(270,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(2097,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(2955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(1492,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1434,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).
thf(4805,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(515,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
thf(2669,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1140,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(4139,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel_0) ).
thf(1771,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(624,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(2943,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(954,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).
thf(3710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1112,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(4073,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(1801,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1148,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(4154,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1247,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Power_Opower__class_Opower @ B @ C @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__power__if_0) ).
thf(4374,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Power_Opower__class_Opower @ B @ C @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(725,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
thf(3182,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(604,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(2896,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(595,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(2871,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(1306,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(4509,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(1127,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(4107,plain,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
thf(1969,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1272,axiom,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_Int_Oint )
= ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transfer__int__nat__numerals_I4_J_0) ).
thf(4430,plain,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_Int_Oint )
= ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).
thf(2261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).
thf(2446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1228,axiom,
class_Int_Onumber @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(4332,plain,
class_Int_Onumber @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(1065,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(3971,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ D ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Suc @ D ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(2553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ D ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Suc @ D ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(92,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
thf(1688,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(741,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(3219,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(577,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(2824,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1169,axiom,
( c_Int_OPls
= ( c_Int_OBit0 @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_1) ).
thf(4203,plain,
( c_Int_OPls
= ( c_Int_OBit0 @ c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__divide_0) ).
thf(1877,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(970,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel1_0) ).
thf(3747,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).
thf(2605,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(658,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(3027,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).
thf(2343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(936,axiom,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(3668,plain,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
thf(1993,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1441,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(4818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(1107,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
thf(4064,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(1630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
thf(1909,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1476,axiom,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(4897,plain,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(717,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(3165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(1862,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1068,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(3977,plain,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(615,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(2923,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(912,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__if_0) ).
thf(3614,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(2785,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1456,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(4850,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(774,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(3298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1368,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ ( c_Suc @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div2__Suc__Suc_0) ).
thf(4652,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ ( c_Suc @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(1556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).
thf(2542,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(2289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(2252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).
thf(2664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1020,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_1) ).
thf(3861,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(1383,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__power2_0) ).
thf(4684,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(711,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(3150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(2329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1325,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
thf(4554,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(1820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(856,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
thf(3480,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(196,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(1926,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
thf(4232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(1594,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
thf(2086,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1043,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ D @ A ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
thf(3917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ D @ A ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(945,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(3687,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(2931,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(653,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_2) ).
thf(3016,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(334,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(2244,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(4304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(1726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1301,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(4497,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
thf(2999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1109,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
thf(4067,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(2069,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(2075,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(2418,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1397,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__iszero__Numeral1_0) ).
thf(4720,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
thf(1841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(2439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(321,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ E @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(2212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ E @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(918,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).
thf(3627,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(555,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( D
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(2765,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( D
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(831,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(3423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(2481,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(1117,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power3__eq__cube_0) ).
thf(4085,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(715,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).
thf(3159,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(2369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_0) ).
thf(4362,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(498,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(2633,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(780,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(3310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(1496,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1165,axiom,
! [A: $i] :
( ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc3__eq__add__3_0) ).
thf(4196,plain,
! [A: $i] :
( ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(2303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1039,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(3908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(1027,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(3876,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(1694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(2693,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1172,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__one__odd__power_0) ).
thf(4209,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ B @ A )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(217,axiom,
class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
thf(1973,plain,
class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1294,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Otimes__class_Otimes @ B @ E @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ D @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
thf(4481,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Otimes__class_Otimes @ B @ E @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ D @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(1805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
thf(2506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(811,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(3380,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1405,axiom,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(4741,plain,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(2952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(729,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(3193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(1051,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(3936,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1464,axiom,
class_Int_Onumber @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
thf(4868,plain,
class_Int_Onumber @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(1905,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(2037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
thf(1684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(844,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(3455,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1337,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(4581,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(1239,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__2__gt__zero_0) ).
thf(4355,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1398,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).
thf(4722,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(1437,axiom,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(4812,plain,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(1015,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(3849,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).
thf(2005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(1029,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
thf(3881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(1626,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(874,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(3522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(2054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1270,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(4426,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(1262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ tc_nat ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
thf(4405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ tc_nat ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(660,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(3031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(2816,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(1385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__odd__eq_0) ).
thf(4690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1258,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__eq_0) ).
thf(4394,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(1276,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_2) ).
thf(4441,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(1139,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__not__even__div2_0) ).
thf(4136,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(2614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1472,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I110_J_0) ).
thf(4886,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(1438,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(4813,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(1336,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(4580,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(643,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).
thf(2994,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ A @ tc_Int_Oint )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ B @ tc_Int_Oint ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_0) ).
thf(2318,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ A @ tc_Int_Oint )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ B @ tc_Int_Oint ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(818,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(3395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).
thf(4052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(2124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1222,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(4319,plain,
class_Power_Opower @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(1209,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(4292,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(1509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1157,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(4177,plain,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
thf(2629,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(2927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(1067,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(3975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(225,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__one_0) ).
thf(1990,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(667,axiom,
class_Ring__and__Field_Ocomm__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring) ).
thf(3048,plain,
class_Ring__and__Field_Ocomm__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1330,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power2_0) ).
thf(4566,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
thf(2684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(2202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).
thf(2333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(586,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(2846,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(477,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(2582,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(894,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(3571,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1073,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(3988,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
thf(2661,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1200,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__minus_0) ).
thf(4272,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(738,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
thf(3214,plain,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
thf(2012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(973,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(3754,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1008,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(3833,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(1248,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(4377,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(599,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(2882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1098,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
thf(4045,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(1372,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).
thf(4658,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(1547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
thf(1748,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(1798,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).
thf(2298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(816,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(3391,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(924,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
thf(3640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(592,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
thf(2863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(782,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(3315,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(389,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(2375,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(683,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(3082,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1378,axiom,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root1_0) ).
thf(4673,plain,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(2732,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(1941,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(848,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).
thf(3462,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(702,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(3129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1057,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(3949,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(1309,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(4517,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1363,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(4641,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(1207,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).
thf(4287,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(4469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(131,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(1780,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(576,axiom,
! [A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) @ tc_nat )
= A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__div__two__times__two_0) ).
thf(2821,plain,
! [A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) @ tc_nat )
= A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(1753,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(2386,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(909,axiom,
class_Ring__and__Field_Odvd @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Odvd) ).
thf(3608,plain,
class_Ring__and__Field_Odvd @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(2160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1342,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(4593,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(2888,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(4522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(925,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(3642,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(301,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(2165,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(675,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
thf(3063,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(884,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(3544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(916,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
thf(3623,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(980,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(3769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(509,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
thf(2656,plain,
class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(682,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(3080,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(8,axiom,
class_Ring__and__Field_Oabs__if @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).
thf(1499,plain,
class_Ring__and__Field_Oabs__if @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1185,axiom,
! [A: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).
thf(4240,plain,
! [A: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).
thf(2092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(2224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(422,axiom,
! [A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_1) ).
thf(2454,plain,
! [A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(146,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(1813,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).
thf(2688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(959,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
thf(3722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1088,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(4020,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(657,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
thf(3026,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
thf(2429,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1144,axiom,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root0_0) ).
thf(4145,plain,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(1004,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(3823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add_0) ).
thf(2337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(2276,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(994,axiom,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
thf(3801,plain,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1138,axiom,
! [B: $i,A: $i] :
( ( ( c_Int_OBit1 @ A )
!= ( c_Int_OBit1 @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).
thf(4132,plain,
! [B: $i,A: $i] :
( ( ( c_Int_OBit1 @ A )
!= ( c_Int_OBit1 @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
thf(1658,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(365,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(2322,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1538,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
thf(2701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1014,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
thf(3847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(2903,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(1424,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(4781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(801,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
thf(3359,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(246,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(2044,plain,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(4117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(1579,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(1738,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A )
= C )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
thf(3041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A )
= C )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_1) ).
thf(4164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).
thf(2354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ A ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
thf(1934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ A ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(862,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(3493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
thf(2379,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(534,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(2711,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
thf(2579,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(743,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(3224,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(1504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(873,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).
thf(3520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(2266,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1257,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(4392,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(518,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(2675,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(252,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(2056,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(335,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).
thf(2247,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(2411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(860,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(3488,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1432,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(4802,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(693,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(3107,plain,
class_Int_Oring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1104,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(4057,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
thf(1898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(162,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(1849,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(929,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(3652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
thf(2838,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(467,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(2558,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(2426,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
thf(2992,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1188,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__add__1_0) ).
thf(4246,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(800,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).
thf(3356,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1297,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(4488,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= B )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).
thf(2975,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= B )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).
thf(2279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1409,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).
thf(4748,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
thf(1955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(585,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
thf(2843,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_0) ).
thf(4235,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(46,axiom,
class_Divides_Oring__div @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).
thf(1585,plain,
class_Divides_Oring__div @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1358,axiom,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat )
= ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__2__eq__2_0) ).
thf(4634,plain,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat )
= ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(1387,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(4695,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(1670,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
thf(2860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(626,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= C )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(2949,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= C )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(1054,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(3943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_1) ).
thf(4838,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(756,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(3256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(1129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ B @ A ) @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__sum_0) ).
thf(4111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ B @ A ) @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(1265,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(4414,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(843,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
= ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(3452,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
= ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(845,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(3457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(677,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
thf(3067,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1419,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(4770,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(2885,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(630,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
thf(2960,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(2347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(2209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(672,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
thf(3056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1048,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
thf(3929,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(2865,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(202,axiom,
class_Int_Onumber @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
thf(1940,plain,
class_Int_Onumber @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(414,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(2435,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(553,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(2760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(835,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(3433,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1323,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(4548,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(1203,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(4278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).
thf(1839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(899,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(3584,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1457,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__numeral__1_0) ).
thf(4851,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(1348,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_1) ).
thf(4606,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(821,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(3401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1400,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_1) ).
thf(4727,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(2088,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I37_J_0) ).
thf(4325,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).
thf(2045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(206,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).
thf(1949,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(1416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I36_J_0) ).
thf(4763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(1267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ B @ A ) @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__diff_0) ).
thf(4419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ B @ A ) @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
thf(1834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1371,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mod__eq__add3__mod__number__of_0) ).
thf(4656,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(879,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(3533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(841,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_0) ).
thf(3447,plain,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(2310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(1844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1026,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(3874,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(2611,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(2325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1047,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
thf(3928,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1161,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(4185,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(917,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(3625,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(960,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(3725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(546,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(2743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(644,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(2997,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
thf(2490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1125,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
thf(4102,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(795,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(3346,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1081,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).
thf(4006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(2110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(784,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(3320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(2305,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(613,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
thf(2919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(1154,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power2_0) ).
thf(4170,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(1286,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(4463,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(1734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_0) ).
thf(4310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(1106,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
thf(4061,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(1401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_3) ).
thf(4730,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(663,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(3039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1334,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
thf(4574,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(992,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).
thf(3797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(902,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(3593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(1646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(962,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(3729,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(532,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(2707,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
thf(2167,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(1005,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(3825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(1375,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
thf(4666,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(1289,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(4468,plain,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(4681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(812,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).
thf(3383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(791,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(3336,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(2971,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(1854,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(453,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_0) ).
thf(2526,plain,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(684,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(3085,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(849,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).
thf(3465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_0) ).
thf(2591,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(2594,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
thf(2174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(2283,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(2389,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(2098,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(858,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(3484,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(989,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__minus1_0) ).
thf(3789,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(1639,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1135,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(4126,plain,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1097,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(4042,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1321,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(4542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(572,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
thf(2811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(1395,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(4715,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(66,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1629,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(2026,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(919,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
thf(3630,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(890,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(3561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(488,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
thf(2608,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(747,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A )
= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(3235,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(2431,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(865,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(3501,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(647,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(3003,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
thf(1822,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1083,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(4010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(1448,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__div__2__gt__zero_0) ).
thf(4834,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(1391,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).
thf(4705,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(1019,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(3859,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(705,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(3136,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(806,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult1__eq_0) ).
thf(3368,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1558,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(296,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ F @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(2152,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ F @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_5) ).
thf(4745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(786,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(3324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= B )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).
thf(2912,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= B )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1028,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(3879,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1414,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(4759,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(2198,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(877,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
thf(3529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(2362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
thf(1607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1278,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2__right_0) ).
thf(4446,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(1893,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(2315,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(1123,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(4098,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(887,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(3552,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(1614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(2009,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1160,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(4182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(1689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(2081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(724,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
thf(3181,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).
thf(2475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1013,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
thf(3844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(505,axiom,
class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
thf(2648,plain,
class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(834,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(3430,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1341,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__ge__zero_0) ).
thf(4591,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(905,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ D @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
thf(3598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ D @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(2462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(1421,axiom,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).
thf(4774,plain,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1213,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).
thf(4299,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(1253,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(4387,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(2576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(1293,axiom,
( ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ tc_Int_Oint )
!= ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of__Pls__Min_0) ).
thf(4478,plain,
( ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ tc_Int_Oint )
!= ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(1075,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).
thf(3993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(1513,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1465,axiom,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(4869,plain,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(612,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(2917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1090,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
thf(4025,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(2779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(1353,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__numeral__1_0) ).
thf(4619,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
thf(2517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(952,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(3705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(479,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(2587,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(906,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(3601,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(759,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).
thf(3264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(175,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1876,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).
thf(1673,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(703,axiom,
! [B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).
thf(3132,plain,
! [B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1344,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).
thf(4597,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(1244,axiom,
class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(4367,plain,
class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(733,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).
thf(3203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(851,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
thf(3469,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).
thf(2003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(291,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(2142,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(932,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(3658,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(2218,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
thf(2258,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1470,axiom,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__1_0) ).
thf(4880,plain,
! [A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(1096,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__one__odd__power_0) ).
thf(4039,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(72,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(1642,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).
thf(2102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1440,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
thf(4816,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(1085,axiom,
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__1__nat_0) ).
thf(4014,plain,
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(43,axiom,
class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
thf(1578,plain,
class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= C )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= C )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1130,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(4114,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(4472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(1260,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
thf(4399,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(1384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(4687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(1377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(4670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(987,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(3785,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1249,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_0) ).
thf(4378,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
thf(2534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(2255,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(771,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
thf(3291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(1077,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__pos_0) ).
thf(3997,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__power__if_1) ).
thf(4809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(2983,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(808,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(3373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1010,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(3837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(1427,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
thf(4787,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(1452,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(4841,plain,
class_Divides_Osemiring__div @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__power_0) ).
thf(1986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(1757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1240,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2__right_0) ).
thf(4357,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(863,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A )
= C )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).
thf(3496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A )
= C )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(556,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(2768,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(946,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(3690,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(549,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(2751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1412,axiom,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(4755,plain,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(889,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
thf(3558,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(1789,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(267,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(2091,plain,
class_Orderings_Opreorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__neg__div_0) ).
thf(2795,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1164,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__power__le__0__imp__0_0) ).
thf(4193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ C @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).
thf(2040,plain,
! [B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(374,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).
thf(2340,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(2651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1070,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(3982,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(709,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(3145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1092,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(4029,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1158,axiom,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(4178,plain,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(788,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(3328,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(1035,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
thf(3897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(224,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
thf(1989,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1101,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(4051,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(1237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(4350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(148,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(1816,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(6,axiom,
class_Ring__and__Field_Olordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).
thf(1495,plain,
class_Ring__and__Field_Olordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1475,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__div__eq__add3__div_0) ).
thf(4895,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(1204,axiom,
( c_Complex_Oii
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__not__one_0) ).
thf(4281,plain,
( c_Complex_Oii
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1206,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
thf(4286,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(1357,axiom,
! [A: $i] :
( ( c_Int_OBit1 @ A )
!= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).
thf(4631,plain,
! [A: $i] :
( ( c_Int_OBit1 @ A )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(3177,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(996,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(3804,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1149,axiom,
( ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__Min_0) ).
thf(4157,plain,
( ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1116,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mod__eq__add3__mod_0) ).
thf(4083,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Suc @ ( c_Suc @ A ) ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(957,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
thf(3716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(2572,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(2714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(3196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(832,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).
thf(3426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1094,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(4034,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(978,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(3765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(867,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_0) ).
thf(3506,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(1012,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(3843,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(938,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
thf(3673,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
thf(2021,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(2063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(1742,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
thf(2549,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(803,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(3362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(802,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).
thf(3360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1582,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(2467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
thf(1550,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1305,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_Complex_Ocomplex )
= ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ B ) @ C @ tc_Complex_Ocomplex ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel_0) ).
thf(4506,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_Complex_Ocomplex )
= ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ B ) @ C @ tc_Complex_Ocomplex ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(1295,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_0) ).
thf(4484,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
| ~ ( c_Int_Oiszero @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(1447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(4831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(1181,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
thf(4229,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(1031,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(3886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(388,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(2372,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(2241,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__odd__power_0) ).
thf(2127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__power2__lt__zero_0) ).
thf(4848,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(1829,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
thf(2966,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(950,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).
thf(3701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1186,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ B @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2_0) ).
thf(4242,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ B @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1532,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1431,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_1) ).
thf(4799,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(605,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
thf(2898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(826,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(3411,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(2485,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1001,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).
thf(3817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1063,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
| ( B = D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(3965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
| ( B = D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(751,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(3245,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(655,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(3020,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1171,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I40_J_0) ).
thf(4206,plain,
c_Int_OMin != c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(881,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(3538,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(1227,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
thf(4330,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero__iff_0) ).
thf(1713,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
thf(1597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(523,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
thf(2687,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(1880,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(696,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(3113,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(1902,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1235,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(4345,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(1303,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__square__number__of_0) ).
thf(4501,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(1199,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(4271,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(1118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_Power_Opower__class_Opower @ B @ C @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs_0) ).
thf(4088,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_Power_Opower__class_Opower @ B @ C @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).
thf(2138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(793,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_0) ).
thf(3341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(972,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
thf(3753,plain,
class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(854,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ D @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
thf(3474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ D @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(847,axiom,
class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
thf(3461,plain,
class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Int_Oiszero @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__def_0) ).
thf(2563,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Int_Oiszero @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(2059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1050,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).
thf(3933,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(1156,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(4174,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(773,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).
thf(3296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(638,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(2980,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(1212,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos2_0) ).
thf(4298,plain,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(1230,axiom,
! [A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_1) ).
thf(4335,plain,
! [A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(1445,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__less__0_0) ).
thf(4826,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(1370,axiom,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(4655,plain,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(598,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(2879,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(364,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
thf(2321,plain,
class_Ring__and__Field_Omult__mono1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(1653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(744,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
thf(3227,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(204,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(1944,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1390,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__m1__odd_0) ).
thf(4702,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ B @ tc_nat ) ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ c_Int_OMin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(1425,axiom,
( ( c_FFT__Mirabelle_Oroot @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) )
= c_Complex_Oii ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root4_0) ).
thf(4784,plain,
( ( c_FFT__Mirabelle_Oroot @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_nat ) )
= c_Complex_Oii ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(3096,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1017,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(3854,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_1) ).
thf(2206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1418,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__eq__power2_1) ).
thf(4767,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(823,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(3405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
thf(2690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(1565,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(2018,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).
thf(2832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ B @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
thf(1490,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ B @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1411,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(4752,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(1406,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(4742,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(1219,axiom,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat )
= ( c_Suc @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__3__eq__3_0) ).
thf(4313,plain,
( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat )
= ( c_Suc @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(4423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(670,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(3052,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1462,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_2) ).
thf(4863,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_nat ) @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(581,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(2834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).
thf(2351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(1870,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(557,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(2771,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(25688,plain,
$false,
inference(e,[status(thm)],[2163,1665,2094,3883,4094,4899,2876,3397,3581,1982,2544,2331,3566,1549,3172,3873,4188,1586,4201,4560,3962,2295,4571,4450,4464,3008,4824,2131,4909,2072,4262,3661,1767,3399,2263,3930,3666,4022,1729,3434,3167,2921,4290,3477,3698,3979,3863,3830,4877,1818,1686,2250,2077,1750,4226,4339,4075,2395,4391,3912,3108,1591,4215,4747,3681,3990,4037,2512,3072,1924,2117,2940,2104,2808,3905,2644,4515,2495,3230,2381,1808,2659,1618,3285,3460,4807,4697,3959,2671,1544,3910,4603,3012,1971,4614,2854,1692,4408,1486,4532,3649,3044,3781,2146,1507,3276,2195,1705,1788,3217,3794,3439,3049,4739,2035,3367,3365,4870,2740,1867,4220,4528,2184,3175,2448,2933,4638,1872,4650,2627,1919,3253,2459,3414,3121,4294,4435,3577,2042,3370,4047,3350,1914,4198,3140,3809,4249,4386,2216,4343,3634,4142,2763,3915,1782,2227,1576,3249,4371,4266,3513,4679,3308,3947,1650,1645,1601,3281,2400,2067,1529,1967,4322,2819,1803,2136,1518,1703,2531,2405,3221,2603,3046,2269,3574,3821,3089,1832,4568,2703,3891,4637,3248,4238,4539,3442,3938,3029,4866,1792,3644,2735,4563,4422,2698,1660,4070,3116,4151,4761,3061,1907,2501,4654,3617,2444,1860,1511,2274,4778,3776,2682,1826,4130,3542,4275,4766,4428,2745,3713,2356,1922,3099,3517,4617,2049,1609,4317,3951,3835,4390,4771,1847,1545,2420,3840,3385,2857,4353,4862,2169,3638,4179,4664,4492,4622,2635,2929,4675,3470,3312,4551,3902,1568,3734,4368,3014,4141,4265,1773,4383,1815,4460,2989,1963,4793,1778,4302,3866,4253,3268,4008,3258,4756,2829,3322,3524,4583,3199,4857,2451,3527,1682,4556,4432,2456,2007,2178,4411,4205,2237,2616,1946,4903,2105,3075,4072,1811,4018,3393,1911,4454,4600,2782,2893,1632,2469,4001,3670,4733,1858,4147,4815,4724,3621,2925,3973,3569,1677,2540,2555,3300,3923,1960,4115,2335,2777,3152,3771,4162,3986,4842,3712,2483,3036,4643,2804,4892,4628,2718,3378,3389,2508,4718,4751,2367,2437,2618,3739,2281,1896,2190,3421,3685,1886,4504,4364,1622,2424,1526,4307,3676,3756,4536,3243,2286,2639,3606,3211,2392,2154,1521,1696,3184,4475,3510,4065,1604,4604,3857,4216,2204,4589,2574,3186,1708,2641,3450,4199,3984,3169,2646,3852,4531,3531,2364,3995,2047,3318,2232,3054,2083,1736,4100,2496,2621,4059,1868,2061,3550,4172,2000,1636,2589,2705,4466,4016,3603,1502,1487,4091,4521,4836,2441,2673,1900,1723,3261,4712,2601,3827,1519,2596,4397,4609,2133,3233,2937,4449,3134,1824,4284,2150,2032,4821,3814,2986,4661,3664,3339,2015,3286,1883,1560,2958,3403,1951,1888,4776,2200,1656,2327,3727,2653,3271,4295,2464,2758,2873,2433,2477,3137,3499,3065,3750,3349,3894,1624,4402,3535,1836,2181,3050,2345,2313,3763,2492,4104,1634,4461,2112,4080,3033,1740,1573,3799,3595,3445,4027,1983,2946,4248,2709,3102,2631,4012,3941,3001,3968,4123,3105,3467,2300,2498,1541,2157,2840,2115,3482,1762,2100,2377,4668,2801,1794,1953,4512,4108,2973,4486,4789,1856,4636,1587,4525,4693,4845,2724,1719,4227,3632,4095,3746,4840,4883,3205,4219,3087,3018,4898,4676,3143,4860,4276,4545,2240,4191,2349,2108,2551,4320,2798,4333,3954,4049,4518,4301,2023,3326,2323,3179,3407,2561,3094,4167,2868,4389,3596,4315,3010,1700,1937,2172,4648,4054,3428,4444,2666,3555,4457,2649,2978,2472,3294,4736,1744,4804,2519,3743,2851,1932,3819,3540,2566,4120,1874,4259,3215,3703,2968,2504,1776,3611,3656,3486,3654,1588,2536,3126,3787,2836,2487,2598,3059,3354,2900,1668,1974,4347,1852,2813,3760,3409,3692,2052,1599,4902,1715,3333,1979,3005,4416,3920,2272,2140,2756,3162,3201,4223,1759,3147,4535,4148,2788,3802,4625,1563,3306,2748,2402,3508,2529,2546,3563,3279,4212,4889,3587,3999,2963,4906,2915,2408,2793,3190,1515,2221,2189,1616,4004,1996,3675,1732,4572,2909,3807,3707,2292,1698,3871,2585,4594,4874,1927,3289,4269,4489,2121,2235,2144,2936,2729,1648,1764,2413,2677,2176,4708,4872,1680,3491,1483,2570,4256,4438,3375,3888,4577,3792,4359,3111,3274,2524,4453,3343,3158,2260,4786,4144,3387,3504,3900,1965,2695,2827,3213,3741,3547,4341,3070,2727,3768,1916,3636,3925,1784,4494,4077,3811,2791,3240,3609,2849,2657,4159,1620,3472,3736,3758,1929,3945,3283,3266,2514,2568,4032,4709,1535,2806,1795,3590,2398,4328,2716,4381,3868,4612,4251,4537,3773,3646,4822,1997,3123,3783,3416,3304,3091,3302,4245,1675,3023,4558,2193,1786,3118,4127,2029,4096,4796,2891,2308,3077,4645,3695,3330,2738,3208,1865,2753,3436,3619,3579,4854,4640,2358,2148,3719,2510,3678,2521,2538,2415,1574,3732,4586,2065,2079,2361,2721,2119,3352,4337,2679,4498,2478,3251,3155,2229,3238,2214,2383,2624,2637,2422,3957,2774,3683,1524,4828,3515,3779,2906,3419,4699,2097,2955,1492,4805,2669,4139,1771,2943,3710,4073,1801,4154,4374,3182,2896,1571,2871,4509,4107,1969,4430,2261,2446,4332,3971,2553,1688,3219,2824,4203,1877,3747,2605,3027,2129,2343,3668,1993,4818,4064,1630,1909,4897,3165,1862,3977,2923,3614,2785,4850,3298,4652,1556,2542,2289,2252,2664,3861,4684,3150,2329,4554,1820,3480,1926,4232,1594,2086,3917,3687,2931,3016,2244,4304,1726,4497,2999,4067,2069,2075,2418,4720,1841,2439,2212,3627,2765,3423,2481,4085,3159,2369,4362,2633,3310,1496,4196,2303,3908,3876,1694,2693,4209,1973,4481,1805,2506,3380,4741,2952,3193,3936,4868,1905,2037,1684,3455,4581,4355,4722,4812,3849,2005,3881,1626,3522,2054,4426,4405,3031,2816,4690,1662,4394,4441,4136,2614,4886,4813,4580,2994,2318,3395,4052,2124,4319,4292,1509,4177,2629,2927,3975,1990,3048,4566,2684,2202,2333,2846,2582,3571,3988,2661,4272,3214,2012,3754,3833,4377,2882,4045,4658,1547,1748,1798,2298,3391,3640,2863,3315,1611,2375,3082,4673,2732,1941,3462,3129,3949,4517,4641,4287,4469,1780,2821,1753,2386,3608,2160,4593,2888,4522,3642,2165,3063,3544,3623,3769,2656,3080,1499,4240,2092,2224,2454,1813,2688,3722,4020,3026,2429,4145,3823,2337,2276,3801,4132,1658,2322,1538,2701,3847,2903,4781,3359,2044,4117,1579,1738,3041,4164,2354,1934,3493,2379,2711,2579,3224,1504,3520,2266,4392,2675,2056,2247,2411,3488,4802,3107,4057,1898,1849,3652,2838,2558,2426,2992,4246,3356,4488,2975,2279,4748,1955,2843,4235,1585,4634,4695,1670,2860,2949,3943,1717,4838,3256,4111,4414,3452,3457,3067,4770,2885,1553,2960,2347,2209,3056,3929,2865,1940,2435,2760,3433,4548,4278,1839,3584,4851,4606,3401,4727,2088,4325,2045,1949,4763,4419,1834,4656,3533,3447,2310,1844,3874,2611,2325,3928,4185,3625,3725,2743,2997,2490,4102,2187,3346,4006,2110,3320,2305,2919,4170,4463,1734,4310,4061,4730,3039,4574,3797,3593,1646,3729,2707,2167,3825,4666,4468,4681,3383,3336,2971,1854,2526,3085,3465,2591,2594,1721,2174,2283,2389,2098,3484,3789,1639,4126,4042,4542,2811,4715,1629,2026,3630,3561,2608,3235,2431,3501,3003,1822,4010,4834,4705,3859,3136,3368,1558,2152,4745,3324,2912,3879,4759,2198,3529,2362,1607,4446,1893,2315,4098,3552,1614,2009,4182,1689,2081,3181,2475,3844,2648,3430,4591,3598,2462,4774,4299,4387,2576,4478,3993,1513,4869,2917,4025,2779,4619,2517,3705,2587,3601,3264,1876,1673,3132,4597,4367,3203,3469,2003,2142,3658,2218,2258,4880,4039,1642,2102,4816,4014,1578,1957,4114,4472,4399,4687,4670,3785,4378,2534,2255,3291,3997,4809,2983,3373,3837,4787,4841,1986,1757,4357,3496,2768,3690,2751,4755,3558,1789,1710,2091,2795,4193,2040,2340,2651,3982,3145,4029,4178,3328,3897,1989,4051,4350,1816,1495,4895,4281,4286,4631,3177,3804,4157,4083,3716,2572,2714,3196,3426,1891,4034,3765,3506,3843,3673,2021,2063,1742,2549,3362,3360,1582,2467,1550,4506,4484,4831,4229,3886,2372,2241,2127,4848,1829,1977,2966,3701,4242,1532,4799,2898,3411,2485,3817,1500,3965,3245,3020,4206,3538,4330,1713,1597,2687,1880,3113,1902,4345,4501,4271,4088,2138,3341,3753,3474,3461,2563,2059,3933,4174,3296,2980,4298,4335,4826,4655,2879,2321,1653,3227,1944,4702,4784,3096,3854,2206,4767,3405,2690,1565,2018,2832,1490,4752,4742,4313,1769,4423,3052,4863,2834,2351,1870,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV632-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 19 02:28:18 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.73/1.15 % [INFO] Parsing done (280ms).
% 1.73/1.16 % [INFO] Running in sequential loop mode.
% 2.54/1.37 % [INFO] eprover registered as external prover.
% 2.54/1.38 % [INFO] cvc4 registered as external prover.
% 2.54/1.38 % [INFO] Scanning for conjecture ...
% 3.09/1.53 % [INFO] Found a conjecture and 1483 axioms. Running axiom selection ...
% 4.26/1.82 % [INFO] Axiom selection finished. Selected 1481 axioms (removed 2 axioms).
% 5.61/2.14 % [INFO] Problem is propositional (TPTP CNF).
% 5.61/2.16 % [INFO] Type checking passed.
% 5.61/2.17 % [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 ...
% 85.41/18.92 % External prover 'e' found a proof!
% 85.41/18.92 % [INFO] Killing All external provers ...
% 85.41/18.92 % Time passed: 18391ms (effective reasoning time: 17765ms)
% 85.41/18.92 % Solved by 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)>
% 85.41/18.93 % Axioms used in derivation (1481): cls_abs__le__zero__iff_0, cls_mult__eq__1__iff_1, cls_divide__le__eq__number__of_9, cls_root__cancel_0, cls_less__iff__diff__less__0_0, cls_mod__Suc__eq__mod__add3_0, cls_even__add_2, cls_add__0__left_0, cls_le__divide__eq_8, cls_linorder__antisym__conv2_1, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_mult__numeral__1__right_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, cls_le__divide__eq_3, cls_even__sum__nat_2, cls_less__divide__eq_3, cls_divide__le__eq__number__of1_9, cls_zero__less__power__eq_1, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_zero__le__power__iff_2, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_dvd__div__neg_0, cls_minus__le__iff_0, cls_power__0_0, cls_dvd__mult__cancel1_0, cls_lemma__not__even__div2_0, cls_natgb_Oadd__r0__iff_1, cls_divide__eq__eq_3, cls_eq__add__iff2_1, cls_sum__power2__gt__zero__iff_2, cls_neg__0__le__iff__le_1, cls_nat__dvd__not__less_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_order__le__less__trans_0, cls_mult__cancel2_0, cls_add__is__1_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_nat__mult__eq__1__iff_1, cls_Suc__inject_0, cls_dvd__mult2_0, cls_order__eq__iff_0, cls_divide__less__0__iff_0, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, cls_number__of__is__id_0, cls_zero__less__divide__iff_5, cls_of__nat__0_0, cls_mod__mult__mult1_0, cls_less__divide__eq__number__of1_6, cls_nat__dvd__1__iff__1_1, cls_odd__power__less__zero_0, cls_abs__div__pos_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs, cls_zero__le__odd__power_1, cls_of__nat__add_0, cls_abs__if__lattice_0, cls_abs__le__iff_2, cls_dvd_Oantisym__conv_0, cls_odd__add_1, cls_divide__le__eq_2, cls_mult__imp__le__div__pos_0, cls_divide__pos__pos_0, clsarity_Int__Oint__Int_Onumber, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, cls_mult__2__right_0, cls_power2__eq__imp__eq_0, cls_eq__divide__eq__number__of1_4, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_dvd__mult__right_0, cls_DERIV__mult__lemma_0, cls_order__less__le__trans_0, cls_comm__semiring__class_Odistrib_0, cls_mod2__gr__0_0, cls_not__iszero__1_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_even__zero__nat_0, cls_divide__eq__eq__number__of_4, cls_abs__of__nonneg_0, cls_dvd__eq__mod__eq__0__number__of_0, cls_zero__le__even__power_H_0, cls_le__minus__self__iff_0, cls_left__add__mult__distrib_0, cls_mult__less__cancel__right__disj_0, cls_divide__self_0, cls_rel__simps_I43_J_1, cls_mult__nonneg__nonpos2_0, cls_even__even__mod__4__iff_1, cls_one__is__add_4, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_left__minus_0, cls_nat__1__eq__mult__iff_0, cls_square__eq__iff_1, cls_le__divide__eq__number__of1_0, cls_minus__zero_0, cls_power__le__zero__eq__number__of_1, cls_Lim_Ominus__diff__minus_0, cls_mult_Odiff__left_0, clsarity_Int__Oint__Ring__and__Field_Olordered__ring, cls_inverse__zero__imp__zero_0, cls_xt1_I12_J_0, cls_sum__squares__eq__zero__iff_0, cls_negative__imp__inverse__negative_0, clsarity_Int__Oint__Ring__and__Field_Oabs__if, cls_Suc__n__not__n_0, cls_even__mult__two__ex_0, cls_Bit0__Pls_0, cls_divide__le__eq__number__of_4, cls_zero__less__power__eq_5, clsarity_Complex__Ocomplex__Int_Onumber, cls_divide__nonpos__neg_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_nat__mult__div__cancel__disj_0, cls_comp__arith_I112_J_0, cls_number__of__Bit1_0, cls_mult__is__0_2, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_not__iszero__Numeral1_0, cls_dvd__eq__mod__eq__0__number__of_1, cls_add__increasing2_0, cls_divide__numeral__1_0, cls_less__half__sum_0, cls_less__antisym_0, cls_nat__mod__eq__iff_1, cls_divide__less__eq__number__of1_5, cls_le__divide__eq__number__of_6, cls_not__sum__squares__lt__zero_0, 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_iszero__number__of__Bit0_0, cls_inverse__eq__iff__eq_0, cls_abs__diff__triangle__ineq_0, cls_mod__by__0_0, cls_add__is__1_2, cls_power__inject__exp_0, cls_mod__mod__cancel_0, cls_zero__le__mult__iff_3, cls_class__semiring_Osemiring__rules_I29_J_0, cls_abs__triangle__ineq2_0, cls_linorder__neqE_0, cls_transfer__int__nat__numerals_I3_J_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, cls_inverse__le__1__iff_2, cls_less__add__Suc2_0, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, cls_divide__le__eq__number__of1_4, cls_of__nat__less__iff_0, clsarity_Int__Oint__Ring__and__Field_Opordered__ring, cls_less__divide__eq__number__of_8, cls_nonzero__inverse__eq__divide_0, 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cls_power__even__eq_0, cls_sum__power2__gt__zero__iff_0, clsarity_nat__OrderedGroup_Oab__semigroup__mult, cls_less__add__iff1_1, cls_mult__imp__less__div__pos_0, cls_diff__minus__eq__add_0, cls_mult__cancel1_1, cls_divide__zero__left_0, cls_linorder__neqE__ordered__idom_0, cls_class__semiring_Opwr__pwr_0, cls_nonzero__abs__divide_0, cls_le__divide__eq_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_root1_0, cls_div__dvd__div_0, cls_div__add_0, cls_mod__diff__right__eq_0, cls_add__mult__distrib_0, cls_dvd__triv__left_0, cls_class__ringb_Oadd__cancel_0, cls_dvd_Oless__le_0, cls_mult__left__le__one__le_0, cls_add__nonpos__nonpos_0, cls_divide__pos__neg_0, cls_one__less__inverse__iff_2, cls_add__self__div__2_0, cls_mod__add__self1_0, cls_abs__dvd__iff_0, cls_abs__less__iff_0, cls_le__divide__eq__number__of_1, cls_add__nonneg__eq__0__iff_1, cls_sum__power2__eq__zero__iff_1, cls_divide__le__0__iff_1, cls_even__sum__nat_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring, cls_mod__0_0, cls_class__semiring_Osemiring__rules_I3_J_0, cls_one__le__inverse__iff_0, cls_mult__eq__0__iff_2, clsarity_Int__Oint__Orderings_Opreorder, cls_nat__1__eq__mult__iff_1, cls_mult__less__mono1_0, cls_neg__le__0__iff__le_1, cls_mod__mod__trivial_0, cls_less__divide__eq__number__of_6, cls_power2__abs_0, cls_nat_Oinject_0, cls_add__lessD1_0, cls_abs__le__D2_0, cls_less__SucE_0, cls_sum__squares__gt__zero__iff_1, cls_eq__divide__eq_2, cls_order__neq__le__trans_0, cls_power__eq__imp__eq__base_0, cls_natgb_Onoteq__reduce_0, cls_add__nonneg__nonneg_0, cls_class__ring_Oneg__mul_0, cls_neg__one__odd__power_0, cls_divide__eq__eq__number__of_1, clsarity_nat__Ring__and__Field_Osemiring, cls_eq__neg__iff__add__eq__0_1, cls_mult__mono_H_0, cls_power__le__zero__eq_2, clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs, cls_mult__strict__left__mono__comm_0, cls_zero__le__power__eq_0, cls_class__ringb_Oadd__r0__iff_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_abs__mult__self_0, cls_mult__less__cancel__left__neg_1, cls_order__antisym__conv_0, cls_add__numeral__0_0, cls_dvd__minus__iff_0, clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors, cls_divide_Odiff_0, cls_even__less__0__iff_1, cls_division__ring__inverse__add_0, cls_less__divide__eq__number__of1_8, cls_abs__number__of_1, cls_right__diff__distrib__number__of_0, cls_one__dvd_0, cls_le__imp__neg__le_0, cls_power__le__imp__le__base_0, cls_not__less__less__Suc__eq_1, cls_linorder__less__linear_0, clsarity_Int__Oint__Power_Opower, cls_rel__simps_I51_J_0, cls_inverse__negative__iff__negative_0, cls_div__0_0, cls_divide__strict__right__mono__neg_0, cls_abs__not__less__zero_0, cls_add__strict__increasing_0, cls_divide__less__eq_2, cls_dvd__mod__iff_0, cls_power__strict__increasing__iff_1, cls_minus__divide__divide_0, cls_divide__less__0__1__iff_0, cls_divide__le__eq__number__of_7, 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cls_dvd__mult__cancel2_0, cls_xt1_I11_J_0, clsarity_Int__Oint__Ring__and__Field_Oring, cls_abs__divide_0, cls_mult__imp__div__pos__less_0, cls_abs__triangle__ineq_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_less__divide__eq__number__of1_4, cls_mult__le__0__iff_2, cls_divide__less__0__iff_5, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_mult__less__cancel2_0, cls_less__Suc0_0, cls_dvd_Ole__neq__trans_0, cls_divide__less__0__iff_2, cls_div__mult__self2_0, cls_div__mult1__eq_0, clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add, cls_mult__1_0, cls_zmod__simps_I2_J_0, cls_dvd__mult__left_0, cls_mult__less__cancel1_2, cls_nat__numeral__1__eq__1_0, cls_mod__mult__self2__is__0_0, cls_add__mult__distrib2_0, cls_divide__less__eq__number__of_3, cls_neg__less__0__iff__less_1, cls_mod__add__right__eq_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, cls_zero__less__power__eq_2, cls_comm__monoid__add_Omult__left__commute_0, cls_add__frac__num_0, cls_mult__right__mono__neg_0, cls_zero__le__power__iff_0, cls_abs__mult_0, cls_neg__equal__zero_0, cls_sum__squares__eq__zero__iff_2, cls_le__divide__eq__number__of1_3, clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict, cls_diff__divide__distrib_0, cls_add__minus__cancel_0, cls_div__power_0, cls_diff__0__right_0, cls_xt1_I6_J_0, clsarity_Int__Oint__Nat_Osemiring__char__0, cls_positive__imp__inverse__positive_0, cls_le__add__right__mono_0, cls_minus__mult__right_0, cls_inverse__inverse__eq_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_mult__less__cancel__left__disj_3, cls_divide__le__eq__number__of1_1, cls_n__less__m__mult__n_0, cls_zero__less__mult__pos2_0, cls_divide__eq__eq__number__of1_1, cls_mult__left_Ominus_0, cls_divide__left__mono_0, clsarity_Int__Oint__OrderedGroup_Omonoid__mult, cls_mult_Oadd__right_0, cls_dvd__abs__iff_1, cls_nat__mult__div__cancel1_0, cls_mod__mult__mult2_0, cls_mult__1__left_0, cls_one__less__inverse__iff_0, cls_nat_Osimps_I3_J_0, cls_frac__eq__eq_1, cls_abs__number__of_0, cls_linorder__not__le_0, cls_mod2__gr__0_1, clsarity_nat__Ring__and__Field_Omult__mono1, cls_mod__mult__eq_0, cls_minus__le__iff_1, cls_mult__less__cancel__right__disj_4, cls_power__one__right_0, cls_double__add__less__zero__iff__single__less__zero_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors, cls_eq__add__iff2_0, cls_one__less__mult_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_class__semiring_Osemiring__rules_I35_J_0, cls_less__trans__Suc_0, cls_zero__less__divide__1__iff_1, cls_inverse__less__1__iff_1, cls_abs__if_0, cls_zero__le__divide__1__iff_1, cls_abs__power__minus__one_0, cls_power2__eq__square__number__of_0, cls_abs__triangle__ineq3_0, cls_mult__zero__left_0, cls_plus__nat_Oadd__0_0, cls_dvd_Oeq__iff_2, cls_dvd__mult__cancel__right_0, cls_comm__monoid__add_Omult__1_0, cls_odd__add_2, cls_mod__diff__left__eq_0, cls_divide__le__0__iff_4, cls_nat__mult__eq__1__iff_0, cls_div__mult__mult2_0, cls_less__eq__neg__nonpos_0, clsarity_Int__Oint__Ring__and__Field_Oidom, cls_le__divide__eq_9, cls_dvd_Oless__trans_0, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_dvd_Oorder__trans_0, cls_less__divide__eq_6, cls_power__Suc__less__one_0, cls_rel__simps_I44_J_0, cls_neg__0__equal__iff__equal_0, cls_neg__le__iff__le_0, cls_class__fieldgb_Odivide__inverse_0, cls_less__minus__self__iff_1, cls_divide__less__0__iff_1, cls_dvd__mult__cancel1_1, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, cls_order__less__irrefl_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field, clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1, cls_class__semiring_Osemiring__rules_I27_J_0, cls_frac__less2_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_gt__half__sum_0, cls_divide__less__eq__number__of_9, cls_mod__mult__self3_0, cls_divide__le__eq__number__of1_3, cls_one__less__inverse__iff_1, cls_power2__eq__square_0, cls_add__nonneg__eq__0__iff_2, cls_add__is__0_2, cls_le__divide__eq_4, cls_diff__frac__eq_0, cls_power__eq__0__iff_0, cls_eq__eqI_1, cls_dvd__0__right_0, cls_class__semiring_Oadd__c_0, cls_div__add1__eq_0, cls_nonzero__power__divide_0, cls_one__less__power_0, cls_divide__le__eq__number__of1_8, clsarity_Int__Oint__OrderedGroup_Oab__group__add, cls_mult__pos__pos_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_mult__left__le__imp__le_0, cls_dvd_Oneq__le__trans_0, clsarity_Int__Oint__Ring__and__Field_Omult__mono1, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_add__is__1_3, cls_class__semiring_Osemiring__rules_I36_J_0, cls_divide__less__eq__number__of1_4, cls_div__if_0, cls_add__eq__self__zero_0, cls_inverse__less__imp__less__neg_0, cls_zero__less__divide__iff_4, cls_power__less__imp__less__base_0, cls_add__mono_0, cls_mod__less__divisor_0, cls_sum__squares__gt__zero__iff_0, cls_nat__mult__dvd__cancel__disj_2, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring, cls_class__semiring_Osemiring__rules_I8_J_0, cls_inverse__zero_0, clsarity_Int__Oint__Divides_Osemiring__div, cls_le__divide__eq__number__of1_1, cls_add__pos__pos_0, cls_inverse__eq__divide_0, cls_root__unity_0, cls_Suc__eq__plus1_0, cls_divide__le__0__iff_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add, cls_n__not__Suc__n_0, cls_divide_Oadd_0, cls_mult__right__less__imp__less_0, cls_div__2__gt__zero_0, cls_less__minus__self__iff_0, cls_Suc__mod__eq__add3__mod_0, cls_DERIV__inverse__lemma_0, cls_dvd_Oantisym_0, cls_dvd__power_0, cls_power__less__zero__eq__number__of_0, cls_power__inject__base_0, cls_less__divide__eq__number__of_2, cls_inverse__le__imp__le_0, cls_equation__minus__iff_1, cls_mult_Oprod__diff__prod_0, cls_zmod__simps_I1_J_0, cls_less__SucI_0, cls_div2__Suc__Suc_0, cls_divide__less__eq_9, cls_add__neg__nonpos_0, cls_eq__divide__eq__number__of1_0, cls_not__less0_0, cls_mult__divide__mult__cancel__right_0, cls_dvdI_0, cls_frac__less_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add, cls_iszero__number__of__Bit0_1, cls_power__le__zero__eq_4, cls_divide__le__eq_9, cls_abs__leI_0, cls_rel__simps_I47_J_0, cls_class__ringb_Osubr0__iff_1, cls_divide__strict__right__mono_0, cls_nonzero__minus__divide__divide_0, clsarity_Complex__Ocomplex__Power_Opower, cls_zero__le__power__eq_1, cls_nat__0__less__mult__iff_2, cls_zero__le__power__eq__number__of_0, cls_mult__less__cancel__left__disj_2, cls_minus__add_0, cls_power__eq__0__iff__number__of_0, cls_nat__mult__assoc_0, cls_div__Suc_0, cls_mod__div__decomp_0, clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_divide__inverse_0, cls_field__inverse_0, cls_class__semiring_Opwr__mul_0, cls_abs__le__zero__iff_1, cls_odd__1__nat_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_abs__eq__0_1, cls_nat__mult__commute_0, cls_mult__less__cancel__right__disj_1, cls_gcd__lcm__complete__lattice__nat_Obot__least_0, cls_eq__iff__diff__eq__0_1, cls_add__less__cancel__left_0, cls_zmod__simps_I4_J_0, cls_odd__nat__div__two__times__two__plus__one_0, cls_abs__one_0, cls_div__dvd__div_1, cls_abs__inverse_0, cls_right__minus_0, cls_one__is__add_3, cls_minus__dvd__iff_0, cls_divide__less__eq_6, cls_rel__simps_I40_J_0, cls_less__divide__eq__number__of1_9, cls_inverse__mult__distrib_0, cls_Suc__less__eq_0, cls_divide__less__eq_3, cls_even__sum__nat_3, cls_less__divide__eq_0, cls_inverse__less__imp__less_0, cls_divide__less__eq__number__of_2, clsarity_Complex__Ocomplex__RealVector_Oreal__field, cls_sum__power2__eq__zero__iff_2, cls_mult__cancel1_0, cls_inverse__positive__imp__positive_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_even__mult__two__ex_1, cls_divide__eq__eq__number__of_2, cls_mult__eq__self__implies__10_0, cls_eq__divide__eq__number__of_0, cls_le__eqI_1, cls_power2__sum_0, cls_power__minus_0, cls_class__semiring_Opwr__0_0, cls_Bit1__Min_0, cls_mult__eq__0__iff_1, cls_odd__nat__plus__one__div__two_0, cls_le__iff__diff__le__0_1, cls_divide__nonpos__pos_0, cls_add__gr__0_2, cls_add__less__le__mono_0, cls_zero__le__power_0, cls_power__minus1__odd_0, cls_dvd__mod__imp__dvd_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_even__product__nat_0, cls_nonzero__inverse__mult__distrib_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_nonzero__power__inverse_0, cls_order__less__imp__le_0, cls_abs__le__D1_0, cls_le__divide__eq__number__of1_4, cls_minus__equation__iff_1, cls_abs__eq__mult_2, cls_eq__neg__iff__add__eq__0_0, cls_less__divide__eq__number__of_5, cls_even__nat__equiv__def_1, cls_div__mult__mult1__if_0, cls_add__strict__increasing2_0, cls_nat__dvd__1__iff__1_0, cls_semiring__div__class_Omod__div__equality_H_0, cls_Suc__mod__eq__add3__mod__number__of_0, cls_inverse__numeral__1_0, clsarity_Int__Oint__Ring__and__Field_Osemiring__1, cls_div__mult__self1__is__id_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_mult__idem_0, cls_minus1__divide_0, cls_add__gr__0_1, cls_dvd__mult_0, cls_le__imp__inverse__le__neg_0, cls_division__ring__inverse__diff_0, cls_even__nat__plus__one__div__two_0, cls_le__divide__eq__number__of_4, cls_mod__eq__0__iff_1, cls_zero__le__divide__iff_1, cls_power__strict__increasing__iff_0, cls_split__div__lemma_2, cls_mod__if_0, cls_less__Suc0_1, cls_Suc__n__div__2__gt__zero_0, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_divide__less__eq__number__of1_1, cls_termination__basic__simps_I2_J_0, cls_of__nat__Suc_0, cls_class__ringb_Osubr0__iff_0, cls_divide__le__eq__number__of1_0, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, cls_nat__even__iff__2__dvd_1, cls_class__semiring_Omul__pwr_0, cls_zero__less__power__eq__number__of_2, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_eq__iff__diff__eq__0_0, cls_mod__mult2__eq_0, cls_odd__pos_0, cls_divide_Ominus_0, cls_dvd_Ole__less__trans_0, cls_less__divide__eq__number__of1_5, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_natgb_Oadd__mul__solve_1, cls_divide__less__0__1__iff_1, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring, cls_le__divide__eq__number__of1_8, cls_power__Suc__less_0, cls_divide__less__eq__number__of_5, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult, cls_square__eq__iff_0, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_add__numeral__0__right_0, cls_mult__minus1__right_0, cls_xt1_I7_J_0, cls_power2__minus_0, cls_inverse__nonpositive__iff__nonpositive_1, cls_nat__mult__less__cancel1_0, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_zero__less__power__eq__number__of_5, cls_linorder__not__less_1, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_le__add__iff2_0, cls_not__one__le__zero_0, cls_mult__less__le__imp__less_0, cls_nat__less__le_1, cls_zero__le__power2_0, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, cls_rel__simps_I48_J_0, cls_mod__self_0, cls_less__eqI_1, cls_zero__le__imp__of__nat_0, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_neg__less__iff__less_0, cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0, cls_le__divide__eq__number__of_0, cls_Suc__div__eq__add3__div__number__of_0, cls_divide__less__0__iff_4, cls_split__mult__neg__le_1, cls_class__semiring_Osemiring__rules_I22_J_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, cls_power__mono_0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_even__less__0__iff_0, cls_mult__left_Oadd_0, cls_comp__arith_I110_J_0, cls_rel__simps_I46_J_0, cls_divide__le__eq__number__of_3, clsarity_Int__Oint__Ring__and__Field_Oordered__idom, cls_power__le__zero__eq__number__of_3, cls_power__0__left_1, cls_le__divide__eq__number__of_9, cls_sum__squares__le__zero__iff_0, cls_less__divide__eq__number__of_9, cls_abs__triangle__ineq4_0, cls_mod__Suc__eq__Suc__mod_0, cls_iszero__0_0, cls_less__2__cases_0, cls_add__le__cancel__right_0, cls_mult__right_Odiff_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_dvd__eq__mod__eq__0_1, cls_mult__eq__1__iff_2, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_abs__of__neg_0, cls_abs__less__iff_1, cls_mult__less__cancel__left__pos_0, cls_nat__add__commute_0, cls_Deriv_Oadd__diff__add_0, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1, cls_divide__le__eq__number__of_6, cls_less__divide__eq__number__of1_1, cls_rel__simps_I43_J_0, cls_abs__diff__less__iff_0, cls_zero__le__mult__iff_2, cls_dvd__0__left_0, cls_abs__power2_0, cls_mod__mult__distrib_0, cls_numeral__1__eq__Suc__0_0, cls_divide__le__eq_1, cls_of__nat__less__0__iff_0, cls_div__Suc__eq__div__add3_0, cls_divide__le__0__1__iff_0
% 85.41/18.93 % No. of inferences in proof: 2965
% 85.41/18.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18391 ms resp. 17765 ms w/o parsing
% 86.84/19.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 86.84/19.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------