%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV633-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:06 AM UTC 2026
% Result : Unsatisfiable 33.61s 10.57s
% Output : Refutation 36.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1482
% Syntax : Number of formulae : 2965 ( 525 unt; 0 typ; 0 def)
% Number of atoms : 8863 (1816 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 47250 (5370 ~;5898 |; 0 &;35982 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 100 usr; 10 con; 0-3 aty)
% Number of variables : 7512 ( 0 ^;7512 !; 0 ?;7512 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_FFT__Mirabelle_Oroot_decl,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Int_Onumber__class_Onumber__of_decl,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(c_Int_OBit0_decl,type,
c_Int_OBit0: $i > $i ).
thf(c_Int_OBit1_decl,type,
c_Int_OBit1: $i > $i ).
thf(c_Int_OPls_decl,type,
c_Int_OPls: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(v_m_decl,type,
v_m: $i ).
thf(v_i_decl,type,
v_i: $i ).
thf(v_j_decl,type,
v_j: $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(class_OrderedGroup_Opordered__ab__group__add__abs_decl,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
thf(c_HOL_Oabs__class_Oabs_decl,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Olordered__ring_decl,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Oabs__if_decl,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring__abs_decl,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_decl,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(class_Int_Onumber_decl,type,
class_Int_Onumber: $i > $o ).
thf(c_HOL_Oinverse__class_Odivide_decl,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__field_decl,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_decl,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Odiv_decl,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Parity_Oeven__odd__class_Oeven_decl,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(c_HOL_Oinverse__class_Oinverse_decl,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_decl,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_decl,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Odivision__ring_decl,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(c_Int_Oiszero_decl,type,
c_Int_Oiszero: $i > $i > $o ).
thf(class_Ring__and__Field_Oring__1_decl,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_Int_OMin_decl,type,
c_Int_OMin: $i ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_decl,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Odvd_decl,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_decl,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_decl,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_Nat_Osemiring__char__0_decl,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_RealVector_Oreal__field_decl,type,
class_RealVector_Oreal__field: $i > $o ).
thf(class_Int_Oring__char__0_decl,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Omult__mono_decl,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Complex_Oii_decl,type,
c_Complex_Oii: $i ).
thf(c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1_decl,type,
c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1: $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(1277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).
thf(4447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(1029,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
thf(3883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(2612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(559,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
thf(2778,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(1194,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus1__odd_0) ).
thf(4262,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(1475,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__div__eq__add3__div_0) ).
thf(4899,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(2412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(2427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1046,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(3927,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(1381,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
thf(4682,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).
thf(2280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(2199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(655,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(3021,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(1665,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(576,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__div__two__times__two_0) ).
thf(2822,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
thf(2630,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(1024,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
thf(3873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1161,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(4188,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(47,axiom,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
thf(1586,plain,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1166,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(4201,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(2452,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(546,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(2744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(1447,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(4835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
| ~ ( A @ class_Nat_Osemiring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(2889,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
| ~ ( A @ class_Nat_Osemiring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
thf(1823,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(2306,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(794,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(3345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(1285,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
thf(4464,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(374,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).
thf(2341,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1331,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_5) ).
thf(4571,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(670,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(3053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(2336,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(2109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(819,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(3399,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1047,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
thf(3930,plain,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(934,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(3666,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1088,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(4022,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(1729,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1207,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).
thf(4290,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1068,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(3979,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(2463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(818,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(3397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
thf(1899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).
thf(1840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(897,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(3581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__power2__lt__zero_0) ).
thf(4852,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(1020,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_1) ).
thf(3863,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(2595,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(162,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(1850,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(2499,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(467,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(2559,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(841,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_0) ).
thf(3449,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
thf(1956,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(206,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_Int_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).
thf(1950,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_Int_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(30,axiom,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).
thf(1549,plain,
tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1073,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(3990,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(2210,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(1112,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(4075,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(2622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(999,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arith__simps_I31_J_0) ).
thf(3813,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1040,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(3912,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(693,axiom,
tc_Int_Oint @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(3108,plain,
tc_Int_Oint @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(582,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(2837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
thf(1793,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(811,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(3382,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(2,axiom,
tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
thf(1486,plain,
tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(2363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(1855,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(941,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(3680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(1750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(726,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).
thf(3185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(359,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Suc @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__div__lemma_2) ).
thf(2309,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Suc @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).
thf(2976,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(782,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(3317,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(1178,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_0) ).
thf(4226,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(1301,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(4500,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(976,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(3762,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1307,axiom,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__exhaust__less__4_0) ).
thf(4515,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(2062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(885,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
thf(3549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(767,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).
thf(3285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(809,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(3377,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(453,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_0) ).
thf(2527,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(663,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(3040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(712,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__div__two__times__two__plus__one_0) ).
thf(3153,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(2953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(2590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(625,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(2947,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1060,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
thf(3959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(335,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).
thf(2248,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(27,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).
thf(1544,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(518,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(2676,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1039,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(3910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(1392,axiom,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(4711,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(1345,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__even__div2_0) ).
thf(4603,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(2099,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(2282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).
thf(1591,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(863,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).
thf(3498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(1173,axiom,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I50_J_0) ).
thf(4215,plain,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
thf(2380,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).
thf(1692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( C = D )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
thf(4408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( C = D )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(1295,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_0) ).
thf(4487,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(1340,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_2) ).
thf(4592,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(739,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(3217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(990,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_1) ).
thf(3794,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs_0) ).
thf(4090,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(1333,axiom,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit1__Min_0) ).
thf(4575,plain,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(2316,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(791,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(3338,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).
thf(2141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(984,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(3781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
thf(3253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
thf(2580,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(2901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1273,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__gr__0_1) ).
thf(4435,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1414,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(4762,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(100,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(1705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(653,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_2) ).
thf(3017,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(667,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring) ).
thf(3049,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(968,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(3745,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1403,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(4739,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(647,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(3004,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(789,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).
thf(3332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(804,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(3367,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(927,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(3648,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(704,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).
thf(3135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1121,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(4097,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1470,axiom,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__1_0) ).
thf(4884,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(1463,axiom,
( ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Int_Oint @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transfer__int__nat__numerals_I3_J_0) ).
thf(4870,plain,
( ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Int_Oint @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(612,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(2918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1128,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).
thf(4110,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(4528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
thf(2434,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(534,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(2712,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(912,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__if_0) ).
thf(3616,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__less__imp__less_0) ).
thf(4279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).
thf(2476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
thf(2168,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(1954,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(585,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
thf(2844,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(763,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
thf(3276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
thf(2575,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(806,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult1__eq_0) ).
thf(3370,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(691,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( E @ ( A @ ( F @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
thf(3103,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( E @ ( A @ ( F @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(918,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).
thf(3629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(2348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(2432,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
thf(2491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(1576,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = D )
| ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(4679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = D )
| ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(3088,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(2886,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(2082,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1222,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(4322,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(1287,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_2) ).
thf(4467,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(903,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def2_1) ).
thf(3597,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(2869,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1251,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_1) ).
thf(4386,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(790,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
thf(3335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(1098,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
thf(4047,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(1428,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).
thf(4792,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
thf(1835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1140,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(4142,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).
thf(2046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(2972,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(920,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(3634,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1245,axiom,
! [A: $i] :
( ( A = c_Int_OPls )
| ( ( A @ c_Int_OBit0 )
!= c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I44_J_0) ).
thf(4371,plain,
! [A: $i] :
( ( A = c_Int_OPls )
| ( ( A @ c_Int_OBit0 )
!= c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(1114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(4079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(778,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
thf(3308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(2010,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
thf(1935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1055,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(3947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1431,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_1) ).
thf(4803,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(73,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Obot__least_0) ).
thf(1645,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(765,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
thf(3281,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(997,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(3809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(2173,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(1347,axiom,
( c_Int_OMin
= ( c_Int_OMin @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_1) ).
thf(4607,plain,
( c_Int_OMin
= ( c_Int_OMin @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(577,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(2825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(1529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1027,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(3878,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(17,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).
thf(1518,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1188,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__add__1_0) ).
thf(4249,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).
thf(1887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(945,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(3689,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(862,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(3495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(1871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(2217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(710,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(3148,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1511,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(2185,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(604,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(2897,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(994,axiom,
tc_Int_Oint @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
thf(3803,plain,
tc_Int_Oint @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1416,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I36_J_0) ).
thf(4766,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
thf(2571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1185,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).
thf(4243,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1358,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__2__eq__2_0) ).
thf(4637,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(508,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( tc_Int_Oint @ ( A @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( tc_Int_Oint @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_int__int__eq_0) ).
thf(2654,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( tc_Int_Oint @ ( A @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( tc_Int_Oint @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1183,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_0) ).
thf(4238,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(1318,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
thf(4539,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(758,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(3263,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(741,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(3221,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
thf(2328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(611,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(2916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(1311,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(4524,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(1051,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(3938,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(729,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(3195,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(1235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(4348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(831,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= C )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(3425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= C )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(1461,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(4866,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(1474,axiom,
! [A: $i] :
( ( c_Int_OMin = A )
| ( c_Int_OMin
!= ( A @ c_Int_OBit1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_0) ).
thf(4896,plain,
! [A: $i] :
( ( c_Int_OMin = A )
| ( c_Int_OMin
!= ( A @ c_Int_OBit1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(925,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(3644,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(573,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_1) ).
thf(2814,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1328,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(4563,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(1267,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__diff_0) ).
thf(4422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(122,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(1760,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(1660,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(514,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(2667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(1146,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(4151,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(532,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(2708,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(1002,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(3821,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(882,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(3542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1200,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__minus_0) ).
thf(4275,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(970,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel1_0) ).
thf(3749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1012,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(3845,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(468,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_2) ).
thf(2562,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(436,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).
thf(2488,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1545,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
thf(2691,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = D )
| ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(4353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = D )
| ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(1351,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(4617,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(1373,axiom,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).
thf(4664,plain,
! [B: $i,A: $i] :
( ( A @ c_Int_OBit0 )
!= ( B @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(738,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
thf(3216,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1445,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__less__0_0) ).
thf(4830,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(1195,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).
thf(4265,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(2852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1213,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).
thf(4302,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(1375,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
thf(4669,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(1132,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(4119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(871,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( C @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
thf(3517,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( C @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1892,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(847,axiom,
tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
thf(3463,plain,
tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(812,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).
thf(3385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(2403,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(922,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(3638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1163,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(4194,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(1239,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__2__gt__zero_0) ).
thf(4358,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).
thf(2552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1298,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).
thf(4492,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(388,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(2373,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1353,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__numeral__1_0) ).
thf(4622,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(1043,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
thf(3919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(780,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(3312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(1323,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(4551,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(1036,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).
thf(3902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(963,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(3734,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).
thf(2520,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(541,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__one__even__power_0) ).
thf(2730,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1057,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(3951,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(2024,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1008,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(3835,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).
thf(2301,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1283,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(4460,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(723,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
thf(3180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1253,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(4390,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1289,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(4471,plain,
tc_nat @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1304,axiom,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral1__eq1__nat_0) ).
thf(4507,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(888,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(3557,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1259,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(4400,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(1875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(760,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(3268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1081,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).
thf(4008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(756,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(3258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(784,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(3322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(874,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(3524,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(2794,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1154,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power2_0) ).
thf(4173,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(959,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
thf(3724,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1344,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).
thf(4600,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1138,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).
thf(4134,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Int_OBit1 )
!= ( B @ c_Int_OBit1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(1677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(774,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(3300,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(2073,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_5) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
thf(4411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(626,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(2950,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(1386,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__Suc__0_0) ).
thf(4696,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).
thf(2324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1336,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(4583,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(2027,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1478,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_4) ).
thf(4903,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(274,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(2105,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1110,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(4072,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(1086,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(4018,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(816,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(3393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(1632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1210,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(4297,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
thf(2259,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1078,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(4001,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(936,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(3670,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(1401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_3) ).
thf(4733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(1440,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
thf(4820,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(716,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(3163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
thf(2650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(598,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(2880,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(1682,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(837,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(3438,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1143,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(4147,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
thf(2122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(914,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).
thf(3621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(1065,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(3973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(1978,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(980,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(3771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1150,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_1) ).
thf(4162,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(1015,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(3851,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(1071,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(3986,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).
thf(2833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(954,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).
thf(3712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(557,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(2772,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1442,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(4825,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).
thf(2103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1023,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
thf(3870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
thf(1521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1355,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__power2_0) ).
thf(4628,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
thf(2205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(814,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(3389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(631,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(2964,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1395,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(4718,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(1409,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).
thf(4751,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(880,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(3537,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(1928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(677,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
thf(3068,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1180,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_0) ).
thf(4230,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_1) ).
thf(4842,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
thf(2861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(311,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(2190,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(829,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(3421,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(943,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).
thf(3685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(1303,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__square__number__of_0) ).
thf(4504,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(1796,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(2530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1117,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power3__eq__cube_0) ).
thf(4087,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(2979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(21,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1526,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(4307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(288,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(2137,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(801,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
thf(3361,plain,
tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(973,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(3756,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).
thf(2809,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(2242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
thf(2799,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(743,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(3226,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(1362,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(4643,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
thf(1696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(4475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(478,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(2586,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1115,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(4082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(868,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(3510,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1388,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(4700,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(744,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
thf(3229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(650,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(3011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(1070,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(3984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1314,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_0) ).
thf(4531,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(2118,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1325,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
thf(4557,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(1075,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).
thf(3995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1481,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
thf(4910,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(1636,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(828,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(3418,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(662,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
thf(3037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(1863,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(835,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(3435,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(1604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1035,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
thf(3899,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
thf(2922,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(711,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(3151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(3097,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(865,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(3503,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(1165,axiom,
! [A: $i] :
( ( A @ c_Suc @ c_Suc @ c_Suc )
= ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc3__eq__add__3_0) ).
thf(4199,plain,
! [A: $i] :
( ( A @ c_Suc @ c_Suc @ c_Suc )
= ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(845,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(3459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1473,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(4893,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(1223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
thf(4323,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(609,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(2910,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(4589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(429,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).
thf(2473,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(877,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
thf(3531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(2164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).
thf(1915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).
thf(1708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).
thf(2093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
thf(1783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1244,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(4370,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(978,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(3767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(354,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(2296,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1092,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(4031,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(1736,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1123,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(4100,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(439,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
thf(2496,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(2660,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1104,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(4059,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_2) ).
thf(1768,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(170,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(1868,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(2382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(1723,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1393,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_2) ).
thf(4712,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(1286,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(4466,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(1005,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(3827,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(906,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(3603,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(459,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(2541,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(2277,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1468,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__gr__0_0) ).
thf(4878,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(1348,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_1) ).
thf(4609,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).
thf(2147,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(909,axiom,
tc_Int_Oint @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Odvd) ).
thf(3610,plain,
tc_Int_Oint @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).
thf(2606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1278,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2__right_0) ).
thf(4449,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(983,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
thf(3778,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(342,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( E @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( E @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
thf(2264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( E @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( E @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(2409,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(2733,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1085,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__1__nat_0) ).
thf(4016,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(569,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_2) ).
thf(2805,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(1519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1258,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__eq_0) ).
thf(4397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1190,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(4252,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(2969,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(1233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(4344,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(971,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(3752,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(1310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(4521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(1135,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(4128,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1168,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__even__iff__2__dvd_0) ).
thf(4204,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(621,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(2937,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1204,axiom,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__not__one_0) ).
thf(4284,plain,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1000,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
thf(3816,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(2132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(404,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_1) ).
thf(2414,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(752,axiom,
tc_Int_Oint @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(3250,plain,
tc_Int_Oint @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1149,axiom,
( ( tc_nat @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__Min_0) ).
thf(4160,plain,
( ( tc_nat @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1372,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).
thf(4661,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(734,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(3207,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(397,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__plus__one__div__two_0) ).
thf(2396,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(851,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
thf(3471,plain,
tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(1097,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
= B )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(4044,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
= B )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
thf(1560,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
thf(1938,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(157,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).
thf(1837,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(1920,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1101,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(4053,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(705,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(3137,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(595,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(2872,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(957,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
thf(3718,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(905,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
thf(3600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(488,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
thf(2609,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(2179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).
thf(1656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(321,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(2213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1106,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
thf(4063,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(717,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(3166,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).
thf(2445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(1209,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(4295,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(1454,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(4849,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(2628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(515,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
thf(2670,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(821,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(3403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1398,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).
thf(4725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).
thf(1968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(686,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
thf(3090,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(3198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(2332,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(781,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
thf(3314,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(2820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).
thf(2068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(1819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
thf(1624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(884,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(3546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(708,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(3144,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(1260,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
thf(4402,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(879,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(3535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(1787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1265,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(4417,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(658,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(3028,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(668,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
thf(3050,plain,
tc_Int_Oint @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(1125,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
thf(4104,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(462,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
thf(2547,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).
thf(2344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(960,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(3727,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(545,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(2741,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
thf(1634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).
thf(2228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1048,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
thf(3931,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
thf(1740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
thf(1910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(40,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
thf(1573,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(992,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).
thf(3799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(902,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(3595,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(556,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(2769,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1090,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
thf(4027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(1219,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__3__eq__3_0) ).
thf(4316,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(962,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(3731,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(849,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).
thf(3467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(26,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1541,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(221,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(1983,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__less__dividend_0) ).
thf(1804,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1187,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(4248,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(584,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(2841,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(2359,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(2577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
thf(1970,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(48,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
thf(1587,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(445,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(2509,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__divide_0) ).
thf(1878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1083,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(4012,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(747,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= F )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(3237,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= F )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1433,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(4808,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(334,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(2245,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(856,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
thf(3482,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(2515,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(826,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(3413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel_0) ).
thf(1772,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(699,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
thf(3122,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(641,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(2990,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1306,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(4512,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
thf(2685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(1426,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(4789,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(1270,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(4429,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(2694,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1312,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(4525,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(1385,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__odd__eq_0) ).
thf(4693,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(1452,axiom,
tc_nat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(4845,plain,
tc_nat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
thf(1719,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
thf(2858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(457,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
thf(2537,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(919,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
thf(3632,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(698,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).
thf(3119,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1449,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(4840,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(681,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(3078,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(2638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1127,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(4109,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(733,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).
thf(3205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1175,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__ring__1__class_Opower__minus__even_0) ).
thf(4219,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).
thf(3060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(721,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(3176,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1438,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(4817,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(1378,axiom,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_FFT__Mirabelle_Oroot )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root1_0) ).
thf(4676,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_FFT__Mirabelle_Oroot )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(1013,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
thf(3846,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(579,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(2830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(955,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Ring__and__Field_Odvd__class_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_1) ).
thf(3714,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Ring__and__Field_Odvd__class_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1252,axiom,
tc_nat @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(4389,plain,
tc_nat @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(2419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1162,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).
thf(4191,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(2038,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(894,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(3573,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1050,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).
thf(3935,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(2460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1221,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(4320,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(1227,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
thf(4333,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(1099,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(4049,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1367,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
thf(4653,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(982,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
thf(3775,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(707,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(3141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(597,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(2877,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(1308,axiom,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
thf(4518,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(1212,axiom,
tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos2_0) ).
thf(4301,plain,
tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(786,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(3326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).
thf(1964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(1942,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1044,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(3922,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
thf(3000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(365,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(2323,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(823,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(3407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(735,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(3210,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1396,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__even__power_H_0) ).
thf(4721,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(1152,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_1) ).
thf(4167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1268,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(4425,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(838,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
thf(3441,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(422,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_1) ).
thf(2455,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1408,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(4750,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(1321,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(4545,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_1) ).
thf(2080,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
thf(2053,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).
thf(2196,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
thf(1842,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1405,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(4744,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(660,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(3032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1459,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus1__even_0) ).
thf(4861,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(1365,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_1) ).
thf(4648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(1102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).
thf(4054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(832,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).
thf(3428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(1462,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_2) ).
thf(4867,plain,
! [A: $i] :
( ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(1276,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_2) ).
thf(4444,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div )
| ~ ( A @ class_Int_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0__number__of_1) ).
thf(1889,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div )
| ~ ( A @ class_Int_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1282,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(4457,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(505,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
thf(2649,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1157,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(4180,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(1402,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_3) ).
thf(4736,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(117,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1744,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(749,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
thf(3242,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(1250,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I115_J_0) ).
thf(4384,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc )
= ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(2304,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(987,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(3787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(967,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(3743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).
thf(2355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(2465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(1799,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(205,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(1947,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(1984,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).
thf(1715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(803,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(3364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(950,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).
thf(3703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(1825,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1453,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__2__cases_0) ).
thf(4846,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(910,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_0) ).
thf(3611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(930,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(3656,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(2932,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(858,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(3486,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(2125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(929,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(3654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
thf(1588,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(798,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
thf(3354,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(296,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( F @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(2153,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( F @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(2387,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(979,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
thf(3770,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_0) ).
thf(1668,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(217,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
thf(1974,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(443,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_1) ).
thf(2505,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(1001,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).
thf(3819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).
thf(2006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(440,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
thf(2497,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(1319,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
thf(4540,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(881,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(3540,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(975,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).
thf(3760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(1063,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(3967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(751,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(3247,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(824,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono__even_0) ).
thf(3409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( D @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(555,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(2766,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(946,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(3692,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(2482,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
thf(1599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1477,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(4902,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(675,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
thf(3064,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1193,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B = A )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).
thf(4259,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B = A )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(694,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
thf(3109,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1109,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
thf(4069,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(683,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(3083,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(731,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
thf(3201,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(1177,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs__number__of_0) ).
thf(4223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(2370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(737,axiom,
tc_Int_Oint @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).
thf(3215,plain,
tc_Int_Oint @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(843,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(3454,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(854,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
thf(3476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(225,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__one_0) ).
thf(1991,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(616,axiom,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(2926,plain,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(2203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1017,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(3856,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(2076,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(2089,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(867,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_0) ).
thf(3508,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
thf(2617,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
thf(2662,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(408,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(2423,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(1732,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(972,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
thf(3755,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1316,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).
thf(4535,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(1144,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_FFT__Mirabelle_Oroot )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root0_0) ).
thf(4148,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_FFT__Mirabelle_Oroot )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(498,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(2634,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(2749,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).
thf(1857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(146,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(1814,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1363,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(4644,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
thf(2702,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(890,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(3563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(553,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(2761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1354,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(4625,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(2043,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1172,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__one__odd__power_0) ).
thf(4212,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(725,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
thf(3183,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(599,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(2883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(720,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
thf(3173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(252,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(2057,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(777,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
thf(3306,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(901,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(3592,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(1077,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__pos_0) ).
thf(3999,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).
thf(2368,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(1479,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(4906,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(2440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(1515,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1094,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(4036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
thf(2645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono__odd_0) ).
thf(1616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(643,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).
thf(2995,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add_0) ).
thf(2338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(938,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
thf(3675,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(1906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(1648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(952,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(3707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(702,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(3130,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1391,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B = A )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).
thf(4708,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B = A )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(1248,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(4380,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
thf(3042,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1,negated_conjecture,
( ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( v_j @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_i @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( v_m @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) )
!= ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( v_j @ ( v_i @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( v_m @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1483,plain,
( ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( v_j @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_i @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( v_m @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) )
!= ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( v_j @ ( v_i @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( v_m @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(196,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(1927,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1369,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(4657,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(1255,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(4393,plain,
tc_nat @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(1334,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
thf(4577,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(1197,axiom,
! [A: $i] :
( ( A = c_Int_OMin )
| ( ( A @ c_Int_OBit1 )
!= c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I47_J_0) ).
thf(4269,plain,
! [A: $i] :
( ( A = c_Int_OMin )
| ( ( A @ c_Int_OBit1 )
!= c_Int_OMin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(1296,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__self__div__2_0) ).
thf(4489,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(793,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_0) ).
thf(3343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(932,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(3660,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(229,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__plus__one__div__two_0) ).
thf(2001,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1464,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
thf(4872,plain,
tc_Complex_Ocomplex @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(2904,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(1698,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(466,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(2556,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1130,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(4116,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(800,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).
thf(3358,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(2253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_2) ).
thf(2275,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(2033,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
thf(2149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(1341,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__ge__zero_0) ).
thf(4594,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(536,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__number__of__Min_0) ).
thf(2717,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1032,axiom,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Min_0) ).
thf(3890,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1466,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__mod__add3_0) ).
thf(4874,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(1192,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).
thf(4256,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(1274,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A
= ( tc_nat @ ( A @ c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1 @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__mult__two__ex_0) ).
thf(4438,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A
= ( tc_nat @ ( A @ c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1 @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div )
| ~ ( A @ class_Int_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0__number__of_0) ).
thf(2941,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div )
| ~ ( A @ class_Int_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1429,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
thf(4797,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(485,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(2602,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(965,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(3738,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1231,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
= ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I113_J_0) ).
thf(4340,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
= ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(808,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(3375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1031,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(3888,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(1010,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(3839,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(603,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus1__divide_0) ).
thf(2894,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_0) ).
thf(4365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(389,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(2376,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1280,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I45_J_0) ).
thf(4453,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1196,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(4268,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1133,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(4122,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(1535,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1249,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_0) ).
thf(4381,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(2134,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1096,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__one__odd__power_0) ).
thf(4041,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1141,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(4144,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(807,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(3372,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(813,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(3387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(727,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(3187,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(966,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def2_1) ).
thf(3741,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
thf(1833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(921,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_0) ).
thf(3636,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).
thf(2048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1045,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).
thf(3925,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(622,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__neg_0) ).
thf(2938,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(2225,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1884,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1113,axiom,
! [A: $i] :
( ( tc_Int_Oint @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__is__id_0) ).
thf(4077,plain,
! [A: $i] :
( ( tc_Int_Oint @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(755,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(3255,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(998,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(3811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(748,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).
thf(3240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(563,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
thf(2789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(872,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(3519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
thf(2525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(509,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
thf(2657,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(2188,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(638,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(2981,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(852,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
thf(3472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(2393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(684,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(3086,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(964,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
thf(3736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(682,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(3081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(974,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(3758,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1054,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(3945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(766,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_3) ).
thf(3283,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(759,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).
thf(3266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(517,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
thf(2674,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(2016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(138,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
thf(1795,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1225,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I37_J_0) ).
thf(4328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(1022,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(3868,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1349,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_4) ).
thf(4612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(2817,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(1412,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(4758,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(1417,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__mult__two__ex_1) ).
thf(4769,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(2959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(736,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
thf(3213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(991,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(3796,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(981,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(3773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1062,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(3964,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(926,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(3646,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(227,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
thf(1997,plain,
tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1415,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(4764,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(776,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
thf(3304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(719,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(3170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(1675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(3223,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(2161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1189,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(4251,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1120,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(4096,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(2326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(353,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(2293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(669,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(3051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(928,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(3651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(788,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(3330,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(933,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(3663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1174,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(4218,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(646,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).
thf(3002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1441,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(4822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(836,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(3436,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(2442,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(552,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(2759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(985,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(3783,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(2055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(949,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(3700,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_3) ).
thf(2706,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1007,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(3832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(301,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(2166,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(913,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(3619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(896,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(3579,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(423,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(2457,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1456,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(4854,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
thf(1897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(1360,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(4640,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(2425,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(827,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(3416,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(775,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).
thf(3302,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(892,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(3568,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
thf(4887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(1186,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2_0) ).
thf(4245,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(2573,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( tc_Int_Oint @ ( A @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( tc_Int_Oint @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_0) ).
thf(2319,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( tc_Int_Oint @ ( A @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( tc_Int_Oint @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1272,axiom,
( ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Int_Oint @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transfer__int__nat__numerals_I4_J_0) ).
thf(4433,plain,
( ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Int_Oint @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(2311,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1427,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
thf(4790,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(797,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(3352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).
thf(1853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
thf(2084,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1215,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__even__iff__2__dvd_1) ).
thf(4305,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(761,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(3270,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(692,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(3106,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(1139,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__not__even__div2_0) ).
thf(4139,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = C )
| ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__eq__imp__eq_0) ).
thf(4154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = C )
| ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1419,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(4773,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(715,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).
thf(3160,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(2346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(940,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(3678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(431,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Parity_Oeven__odd__class_Oeven ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
thf(2478,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Parity_Oeven__odd__class_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(753,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half_0) ).
thf(3251,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(295,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(2151,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(502,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(2642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(640,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(2987,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(1894,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(2493,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1352,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).
thf(4620,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(1806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(768,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).
thf(3287,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(942,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(3683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
thf(1524,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1444,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit1_0) ).
thf(4828,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(870,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(3515,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(2284,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(1933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(1492,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).
thf(2299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(4586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(2116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
thf(2839,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(706,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
thf(3138,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1374,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
thf(4667,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(568,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(2802,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(2378,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1246,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).
thf(4374,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(724,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
thf(3182,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(3066,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(899,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(3586,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_Complex_Ocomplex @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) )
= ( tc_Complex_Ocomplex @ ( C @ ( B @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel_0) ).
thf(4509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_Complex_Ocomplex @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) )
= ( tc_Complex_Ocomplex @ ( C @ ( B @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(3219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(2182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(175,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1877,plain,
tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(657,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
thf(3027,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1330,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power2_0) ).
thf(4569,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(1630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq_0) ).
thf(2757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(728,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(3192,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(3006,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(898,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(3583,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1019,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(3861,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(2928,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(635,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(2974,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(92,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
thf(1688,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(572,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
thf(2812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).
thf(2632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(703,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).
thf(3133,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(3055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(2314,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(935,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(3668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(2625,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(2111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(679,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(3073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(2780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(2267,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(340,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
thf(2261,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(1821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1049,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(3932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1279,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(4452,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1170,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(4208,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1158,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(4181,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(661,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(3034,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1067,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(3977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(773,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).
thf(3298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(596,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus__one_0) ).
thf(2874,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(1556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(504,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(2647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(4684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).
thf(1952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1033,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).
thf(3893,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).
thf(2710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1324,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(4554,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(2365,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(917,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(3627,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(581,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(2835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1042,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(3917,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1058,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(3953,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(795,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(3348,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1451,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(4844,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(1446,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).
thf(4832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(1181,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
thf(4232,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(378,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(2350,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(539,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(2725,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(2401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(1594,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(830,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).
thf(3423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
thf(2550,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).
thf(2139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(944,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).
thf(3687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(996,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(3806,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1116,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mod__eq__add3__mod_0) ).
thf(4085,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(714,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).
thf(3159,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(2064,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1241,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__abs_0) ).
thf(4362,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_0) ).
thf(2592,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(549,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(2752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
thf(2022,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(779,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(3310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
thf(2535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
thf(2101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1214,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(4304,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(1726,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
thf(2967,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(2390,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(7,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(1496,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1164,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__power__le__0__imp__0_0) ).
thf(4196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(869,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(3512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(3178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1300,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(4497,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1108,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
thf(4067,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_1) ).
thf(2207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1472,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I110_J_0) ).
thf(4890,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(1026,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(3876,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(1694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1171,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I40_J_0) ).
thf(4209,plain,
c_Int_OMin != c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(2984,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1293,axiom,
( ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Int_Oint @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of__Pls__Min_0) ).
thf(4481,plain,
( ( tc_Int_Oint @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Int_Oint @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(860,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(3490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(810,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_3) ).
thf(3380,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(1028,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(3881,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(4426,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(839,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(3444,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(1809,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1873,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(937,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(3672,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(709,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(3146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(605,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
thf(2899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1229,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).
thf(4336,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(893,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(3571,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1014,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
thf(3849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(1626,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(873,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).
thf(3522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1226,axiom,
! [A: $i] :
( ( tc_Complex_Ocomplex @ ( A @ ( A @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
thf(4331,plain,
! [A: $i] :
( ( tc_Complex_Ocomplex @ ( A @ ( A @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(649,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(3009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1261,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).
thf(4405,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1480,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_1) ).
thf(4907,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(1384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(4690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1256,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(4394,plain,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(1275,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power2_1) ).
thf(4441,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(1758,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1476,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(4901,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(895,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(3576,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).
thf(2665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1436,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__power__if_1) ).
thf(4813,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(1335,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
thf(4580,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(817,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(3395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(1281,axiom,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(4456,plain,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(2652,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(771,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
thf(3293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(1069,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(3981,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
thf(1684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(2449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(1509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1156,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(4177,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(1066,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(3975,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(224,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
thf(1990,plain,
tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1329,axiom,
! [A: $i] :
( ( c_Int_OPls = A )
| ( c_Int_OPls
!= ( A @ c_Int_OBit0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).
thf(4566,plain,
! [A: $i] :
( ( c_Int_OPls = A )
| ( c_Int_OPls
!= ( A @ c_Int_OBit0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(2256,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(1129,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__sum_0) ).
thf(4113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Int_Oiszero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__def_0) ).
thf(2564,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Int_Oiszero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(764,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(3278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__odd__power_1) ).
thf(2597,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1958,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1370,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(4658,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(815,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
thf(3391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
thf(1770,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(2715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(923,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(3640,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).
thf(1961,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1240,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( A @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2__right_0) ).
thf(4360,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( A @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(1460,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__eq__number__of_2) ).
thf(4864,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(4673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(1315,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(4534,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(1056,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(3949,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(1753,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1247,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__power__if_0) ).
thf(4377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).
thf(2689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(1072,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).
thf(3988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(1845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(2513,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).
thf(2567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(1547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
thf(1748,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1011,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(3842,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(695,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(3112,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(2060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1198,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(4272,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(291,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(2143,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1037,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
thf(3904,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(757,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__less_0) ).
thf(3260,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(479,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(2588,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(202,axiom,
tc_Int_Oint @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
thf(1941,plain,
tc_Int_Oint @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(846,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
thf(3462,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(2678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
thf(2518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).
thf(4641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
thf(2175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1205,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod2__Suc__Suc_0) ).
thf(4287,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(1288,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult2__eq_0) ).
thf(4469,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(1410,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(4754,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(908,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult2__eq_0) ).
thf(3608,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(587,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).
thf(2850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).
thf(2569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(267,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(2092,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1030,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(3885,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(613,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
thf(2920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(1087,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
thf(4020,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(1079,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(4003,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(887,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(3554,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(1785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1423,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
thf(4781,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(2468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(956,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(3715,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(654,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(3019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(8,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oabs__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).
thf(1499,plain,
tc_Int_Oint @ class_Ring__and__Field_Oabs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(924,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
thf(3642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1327,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(4561,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(1234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_1) ).
thf(4346,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(1790,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__power_0) ).
thf(1987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1052,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
thf(3940,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(696,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(3114,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(523,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
thf(2688,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(762,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).
thf(3273,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(989,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__minus1_0) ).
thf(3791,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1176,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
thf(4222,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(1869,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power2__le__imp__le_0) ).
thf(4145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1003,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(3823,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(993,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
thf(3801,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(2219,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(220,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(1980,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__odd__power_0) ).
thf(2128,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(1763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(701,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(3127,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(1901,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(883,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(3544,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(4132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
thf(1658,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(364,axiom,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
thf(2322,plain,
tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(25,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1538,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(2486,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_0) ).
thf(4241,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(461,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(2545,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(484,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(2599,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1430,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(4800,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(915,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
thf(3623,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1131,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__numeral__1__eq__1_0) ).
thf(4117,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(1579,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(1738,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(688,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
thf(3095,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(948,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(3697,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(859,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(3488,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(700,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(3124,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1317,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(4538,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1145,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(4150,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1376,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).
thf(4671,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(1264,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).
thf(4414,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(1064,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
thf(3970,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(2113,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1006,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(3829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(1802,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(861,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(3493,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).
thf(2543,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(799,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
thf(3356,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1407,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_5) ).
thf(4748,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).
thf(2357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(2145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(1972,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1126,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_2) ).
thf(4106,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(1504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1271,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(4431,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(1182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
thf(4235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1167,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ( A @ ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_1) ).
thf(4202,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ( A @ ( A @ ( B @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(46,axiom,
tc_Int_Oint @ class_Divides_Oring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).
thf(1585,plain,
tc_Int_Oint @ class_Divides_Oring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(446,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(2511,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(1357,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).
thf(4634,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(1670,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(656,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(3024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1119,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
thf(4093,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(697,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero_0) ).
thf(3117,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(2722,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).
thf(2728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1053,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
thf(3943,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(1232,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_Suc @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__2__eq__Suc_H_0) ).
thf(4342,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_Suc @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
thf(2030,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1061,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(3961,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(678,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
thf(3071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1448,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__div__2__gt__zero_0) ).
thf(4838,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(2892,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(1881,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(2807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(713,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
thf(3156,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1041,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
thf(3914,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1439,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(4819,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(1254,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(4392,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(769,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(3288,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(718,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
thf(3168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1359,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
thf(4639,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(1366,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__div__eq__add3__div__number__of_0) ).
thf(4651,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(842,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_0) ).
thf(3452,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(148,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(1817,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(2194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1160,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(4185,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(131,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(1781,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
thf(2013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(615,axiom,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(2924,plain,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1322,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(4548,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(1206,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
thf(4289,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(1201,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
thf(4278,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(844,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(3457,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1387,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(4698,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).
thf(2352,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(2479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(1346,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(4606,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(891,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(3565,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(820,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(3401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(1399,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(4727,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(900,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).
thf(3589,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1224,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(4325,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(246,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(2045,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(687,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(3092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(1418,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__eq__power2_1) ).
thf(4770,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(1966,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(2696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1151,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
thf(4165,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(578,axiom,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(2828,plain,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1465,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(4873,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(2078,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1266,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(4419,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(878,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
thf(3533,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(840,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).
thf(3447,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(2215,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1326,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(4559,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(916,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
thf(3625,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1364,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__power__less__zero_0) ).
thf(4646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(1124,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_Suc @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__2__eq__Suc_0) ).
thf(4102,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_Suc @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(1080,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(4006,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(783,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).
thf(3320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(1153,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__m1__even_0) ).
thf(4170,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1284,axiom,
tc_nat @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(4463,plain,
tc_nat @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(1866,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(2658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(558,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(2775,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(1734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
thf(4061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(2907,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1217,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I37_J_0) ).
thf(4310,plain,
c_Int_OPls != c_Int_OMin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(564,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(2792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1400,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_1) ).
thf(4730,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(1379,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).
thf(4678,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(1998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1332,axiom,
tc_Complex_Ocomplex @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
thf(4574,plain,
tc_Complex_Ocomplex @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(1646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(961,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_2) ).
thf(3729,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(2273,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1432,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(4806,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(2554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).
thf(2532,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(969,axiom,
tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
thf(3748,plain,
tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1230,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_1) ).
thf(4338,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(746,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(3235,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(1469,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1__right_0) ).
thf(4881,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
thf(2416,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(911,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).
thf(3613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(1482,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(4913,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(270,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(2098,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(857,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add1__eq_0) ).
thf(3484,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( C @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(988,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).
thf(3789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(2855,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(953,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(3709,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(1639,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(2290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1350,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(4615,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(2251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1004,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(3825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(1903,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(2406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(805,axiom,
tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
thf(3369,plain,
tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(1320,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__one__even__power_0) ).
thf(4542,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(1394,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
thf(4715,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(66,axiom,
tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1629,plain,
tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).
thf(2004,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(864,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(3501,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(554,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Int_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__0_0) ).
thf(2764,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Int_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1082,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
thf(4010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(4495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(1390,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__m1__odd_0) ).
thf(4705,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(2130,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1018,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
thf(3859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1558,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(2934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).
thf(2262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(2956,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(1689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(785,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(3324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(1155,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__Suc__eq__div__add3_0) ).
thf(4175,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1413,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power2_0) ).
thf(4759,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(2330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1034,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(3896,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(876,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(3529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(2680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
thf(1607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).
thf(2120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(2019,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1406,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(4745,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).
thf(2447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(624,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Oone__class_Oone ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(2944,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Oone__class_Oone ) )
| ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1159,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__eq__power2_0) ).
thf(4182,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
thf(1861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(393,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(2384,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(1457,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__numeral__1_0) ).
thf(4855,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(947,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(3694,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(2786,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__neg__div_0) ).
thf(2796,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_2) ).
thf(4293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(2399,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).
thf(2041,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(833,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(3430,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).
thf(1777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(4774,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(904,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(3598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1292,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
thf(4478,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).
thf(2066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(939,axiom,
tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
thf(3677,plain,
tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(383,axiom,
tc_Int_Oint @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
thf(2362,plain,
tc_Int_Oint @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(796,axiom,
tc_Int_Oint @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
thf(3351,plain,
tc_Int_Oint @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(1513,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(2095,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1111,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(4074,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).
thf(2230,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(2036,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(2739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(4098,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
thf(1994,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(886,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
thf(3552,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(1614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(407,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(2421,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1095,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( A @ ( F @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(4039,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( A @ ( F @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
!= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
thf(2287,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
!= ( A @ ( C @ c_HOL_Oabs__class_Oabs ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(1774,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(2683,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(951,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).
thf(3705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(986,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(3785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(2233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1342,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(4596,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).
thf(1673,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(2050,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(1297,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(4491,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(1343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(4597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(1243,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
thf(4367,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(850,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(3469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1074,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).
thf(3992,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
thf(1908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(931,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(3658,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(618,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(2930,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1134,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
thf(4125,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(72,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(1642,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1437,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(4816,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(1084,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
thf(4014,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(43,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
thf(1578,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(4472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(1383,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__power2_0) ).
thf(4687,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(2155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(745,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
thf(3232,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(770,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
thf(3291,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1238,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__number__of__Pls_0) ).
thf(4356,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(1076,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(3997,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1038,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).
thf(3907,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(1434,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).
thf(4809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(1021,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(3865,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
thf(2719,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1191,axiom,
! [A: $i] :
( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__number__of__Pls_0) ).
thf(4254,plain,
! [A: $i] :
( ( A @ ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(1435,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__0__le__power__imp__0__le_0) ).
thf(4811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( tc_nat @ ( C @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(451,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).
thf(2522,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(690,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
thf(3100,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1009,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
thf(3837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(848,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).
thf(3464,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
thf(2604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).
thf(2736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(1425,axiom,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_FFT__Mirabelle_Oroot )
= c_Complex_Oii ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root4_0) ).
thf(4787,plain,
( ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_FFT__Mirabelle_Oroot )
= c_Complex_Oii ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(2008,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(732,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(3203,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(3062,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(499,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(2636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(652,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(3015,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__even__power_0) ).
thf(1859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1059,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).
thf(3956,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1203,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(4281,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(1025,axiom,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
thf(3875,plain,
tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).
thf(2746,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(530,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__pos__nat_0) ).
thf(2704,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(855,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(3479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(135,axiom,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).
thf(1789,plain,
tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).
thf(2913,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(2619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
thf(2783,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(1091,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(4029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(787,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(3328,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__lemma_0) ).
thf(2201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1421,axiom,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).
thf(4777,plain,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(4051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(1236,axiom,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Pls_0) ).
thf(4350,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(147,axiom,
tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).
thf(1816,plain,
tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(6,axiom,
tc_Int_Oint @ class_Ring__and__Field_Olordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).
thf(1495,plain,
tc_Int_Oint @ class_Ring__and__Field_Olordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1411,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(4755,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).
thf(2334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(889,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
thf(3560,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= B )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1356,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
thf(4631,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(995,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_1) ).
thf(3804,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1148,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(4157,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1089,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(4024,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(2070,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(630,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
thf(2961,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(659,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).
thf(3030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1093,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(4034,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(977,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(3765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(665,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).
thf(3045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(866,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(3506,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(4318,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(1742,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(198,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1930,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(802,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).
thf(3362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1136,axiom,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I42_J_0) ).
thf(4129,plain,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).
thf(1827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
thf(2430,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1582,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1294,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
thf(4484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
thf(2507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1179,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(4229,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1257,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(4395,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(680,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(3076,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(1302,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1_0) ).
thf(4501,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Int_OMin @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(2270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oinverse__class_Oinverse ) )
= ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(792,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).
thf(3341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(442,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(2502,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(332,axiom,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(2241,plain,
tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(672,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
thf(3057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1532,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(586,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(2847,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(907,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(3605,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(825,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).
thf(3411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(1467,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_0) ).
thf(4876,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
thf(1550,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(477,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(2583,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1107,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
thf(4066,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(1923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(750,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(3245,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1169,axiom,
( c_Int_OPls
= ( c_Int_OPls @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_1) ).
thf(4206,plain,
( c_Int_OPls
= ( c_Int_OPls @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(1371,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mod__eq__add3__mod__number__of_0) ).
thf(4659,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__Suc_0) ).
thf(1925,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Divides_Odiv__class_Omod ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(458,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__1_0) ).
thf(2539,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero__iff_0) ).
thf(1713,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
thf(1597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(592,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
thf(2864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(2699,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(853,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(3474,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1422,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).
thf(4779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(1337,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(4584,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(822,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(3405,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(2866,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(414,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(2436,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
thf(1848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(834,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(3432,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1103,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__add_0) ).
thf(4056,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
thf(2170,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(958,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_4) ).
thf(3721,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(772,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
thf(3296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(1912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(651,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
thf(3013,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(875,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(3526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(2754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1228,axiom,
tc_nat @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(4335,plain,
tc_nat @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(1443,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( A @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2_0) ).
thf(4826,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( A @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(1368,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div2__Suc__Suc_0) ).
thf(4655,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Divides_Odiv__class_Odiv ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(516,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(2672,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(501,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
thf(2640,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(1309,axiom,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(4520,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1199,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(4274,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(1653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
thf(4702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(204,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(1945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1397,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__iszero__Numeral1_0) ).
thf(4723,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_Onumber__class_Onumber__of ) @ c_Int_Oiszero ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(1016,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(3854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1424,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(4784,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(644,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(2998,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(1565,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
thf(1490,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1404,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(4742,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(1218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_0) ).
thf(4313,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( tc_nat @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(415,axiom,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(2438,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(2238,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(2615,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(1917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
thf(2993,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(2191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(2106,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
thf(2087,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1458,axiom,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
thf(4858,plain,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(666,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
thf(3047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
thf(2470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(1211,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_0) ).
thf(4298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(4950,plain,
$false,
inference(e,[status(thm)],[4447,3883,2612,2778,4262,4899,2412,2427,3927,4682,2280,1686,2199,3021,1665,2822,2630,3873,4188,1586,4201,2452,2744,4835,2889,1823,2306,3345,4464,2341,4571,3053,2336,2109,3399,3930,3666,4022,1729,4290,3979,2463,3397,1899,1840,3581,4852,3863,2595,1850,2499,2559,3449,1956,1950,1549,3990,2210,4075,2622,3813,3912,3108,2837,1793,3382,1486,2363,1855,3680,1750,3185,2309,2976,3317,4226,4500,3762,4515,2062,3549,1618,3285,3377,2527,3040,3153,2953,2590,2947,3959,2248,1544,2676,3910,4711,4603,2099,2282,1591,3498,4215,2380,1692,4408,4487,4592,3217,3794,4090,4575,2316,3338,2141,3781,3253,2580,2901,4435,1507,4762,1705,3017,3049,3745,4739,3004,3332,3367,3648,3135,4097,4884,4870,2918,4110,4528,2434,2712,3616,4279,2476,2168,1954,2844,3276,2575,3370,3103,3629,2348,2432,2491,1576,4679,3088,2886,2082,4322,4467,3597,2869,4386,3335,4047,4792,1835,4142,2046,2972,3634,4371,4079,3308,2010,1935,3947,4803,1650,1645,1601,3281,3809,2173,4607,2825,1529,3878,1518,1703,4249,1887,3689,3495,1871,2217,3148,1511,2185,2897,3803,4766,2571,4243,4637,2654,4238,4539,3263,3221,2328,2916,4524,3938,3195,4348,3425,4866,4896,3644,2814,4563,4422,1760,1660,2667,4151,2708,3821,3542,4275,3749,3845,2562,2488,1545,2691,4353,4617,4664,1609,3216,4830,4265,2852,4302,4669,4119,3517,1892,3463,3385,2403,3638,4194,4358,2552,4492,2373,4622,3919,3312,4551,3902,1568,3734,2520,2730,3951,2158,2024,3835,2301,4460,3180,4390,4471,4507,3557,4400,1875,3268,4008,3258,3322,3524,2794,4173,3724,4600,2236,4134,1677,3300,2073,2222,4411,2950,4696,2324,4583,2027,4903,2105,4072,4018,3393,1632,4297,2259,4001,3670,4733,4820,3163,2650,2880,1682,3438,4147,2122,3621,3973,1978,3771,4162,3851,3986,2833,3712,2772,4825,2103,3870,1521,4628,2205,3389,2964,4718,4751,3537,1928,3068,4230,4842,2861,2190,3421,3685,4504,1796,2530,1622,4087,2979,1526,4307,2137,3361,3756,2809,2242,2799,3226,4643,1696,4475,2586,1975,4082,3510,4700,3229,3011,3984,4531,2118,4557,3995,4910,1636,3418,3037,1863,3435,1604,3899,2922,3151,3097,3503,4199,3459,4893,4323,2910,4589,2473,3531,2164,1915,1708,2093,1783,4370,3767,2296,4031,1736,4100,2496,2660,4059,1768,1868,2382,1723,4712,4466,3827,3603,2541,2277,4878,4609,2147,1487,3610,2606,4449,3778,2264,2409,2733,4016,2805,1519,4397,1502,4252,2969,4344,3752,4521,4128,4204,2937,4284,3816,2132,2414,3250,4160,4661,3207,2396,3471,4044,1560,1938,1837,1920,4053,3137,2872,3718,3600,2609,2179,1656,2213,4063,3166,2445,4295,4849,2628,2670,3403,4725,1968,3090,3198,2332,3314,2820,2068,1819,1624,3546,3144,4402,3535,1787,4417,3028,3050,4104,2547,2344,3727,2741,1634,2228,3931,1740,1910,1573,3799,3595,2769,4027,4316,3731,3467,1541,1983,1804,4248,2841,2359,2577,1970,1587,2509,1878,4012,3237,4808,2245,3482,2515,3413,1772,3122,2990,4512,2685,4789,4429,2694,4525,4693,4845,1719,2858,2537,3632,3119,4840,3078,2638,4109,3205,4219,3060,3176,4817,4676,3846,2830,3714,4389,2419,4191,2038,3573,3935,2460,4320,4333,4049,4653,3775,3141,2877,4518,4301,3326,1964,1942,3922,3000,2323,3407,3210,4721,4167,4425,3441,2455,4750,4545,2080,2053,2196,1842,4744,1700,3032,4861,4648,4054,3428,4867,4444,1889,4457,2649,4180,4736,1744,3242,4384,2304,3787,3743,2355,2465,1799,1947,1984,1715,3364,3703,1825,4846,3611,3656,2932,3486,2125,3654,1588,3354,2153,2387,3770,1668,1974,2505,3819,2006,2497,4540,3540,3760,3967,3247,3409,2766,3692,2482,1599,4902,3064,4259,3109,4069,3083,3201,4223,2370,3215,3454,3476,1991,2926,2203,3856,1563,2076,2089,3508,2617,2662,2423,1732,3755,4535,4148,2634,2749,1857,1814,4644,2702,3563,2761,1779,4625,2043,4212,3183,2883,3173,2057,3306,3592,3999,2368,4906,2440,1515,4036,2645,1616,2995,2338,3675,1906,1648,3707,3130,4708,4380,3042,1483,1927,4657,4393,4577,4269,4489,3343,3660,2001,4872,2904,1680,1698,2556,4116,3358,2253,2275,2033,2149,4594,2717,3890,4874,4256,4438,2941,4797,2602,3738,4340,3375,3888,3839,2894,4365,2376,4453,4268,4122,1535,4381,2134,4041,4144,3372,3387,3187,3741,1833,3636,2048,3925,2938,2225,1884,4077,3255,3811,3240,2789,3519,2525,2657,2188,2981,1620,3472,2393,3086,3736,3081,3758,3945,3283,3266,2674,2016,1795,4328,3868,4612,2817,4758,4769,2959,3213,3796,3773,3964,3646,1997,4764,3304,3170,1675,3223,2161,4251,4096,2326,2293,3051,3651,3330,3663,4218,3002,4822,3436,2442,2759,3783,2055,3700,2706,3832,2166,1765,3619,3579,2457,4854,1897,4640,2425,3416,3302,3568,4887,4245,2573,2319,4433,2311,4790,3352,1853,2084,4305,3270,3106,4139,4154,4773,3160,2346,3678,2478,3251,2151,2642,2987,1894,2493,4620,1574,1806,3287,3683,1524,4828,3515,2284,1933,1492,2299,4586,2116,2839,3138,4667,2802,2378,4374,3182,3066,3586,1571,4509,3219,2182,1877,3027,4569,1630,2757,3192,3006,3583,3861,2928,2974,1688,2812,2632,3133,3055,2314,3668,2625,2111,3073,2780,2267,2261,1821,3932,4452,4208,4181,3034,3977,3298,2874,1556,2647,4684,1952,3893,2710,4554,2365,3627,2835,3917,3953,3348,4844,4832,4232,2350,2725,2401,1594,3423,2550,2139,3687,3806,4085,3159,2064,4362,2592,2752,2022,3310,2535,2101,4304,1726,2967,2390,1496,4196,3512,3178,4497,4067,2207,4890,3876,1694,4209,2984,4481,3490,3380,3881,4426,3444,1809,1873,3672,3146,2899,4336,3571,3849,1626,3522,4331,3009,4405,4907,4690,1662,4394,4441,1758,4901,3576,2665,4813,4580,3395,4456,2652,3293,3981,1684,2449,1509,4177,3975,1990,4566,2256,4113,2564,3278,2597,1958,4658,3391,1770,2715,3640,1961,4360,4864,1611,4673,4534,3949,1753,4377,2689,3988,1845,2513,2567,1547,1748,3842,3112,2060,4272,2143,3904,3260,2588,1941,3462,2678,2518,4641,2175,4287,4469,4754,3608,2850,2569,2092,3885,2920,4020,4003,3554,1785,4781,2468,3715,3019,1499,3642,4561,4346,1790,1987,3940,3114,2688,3273,3791,4222,1869,4145,3823,3801,2219,1980,2128,1830,1763,3127,1901,3544,4132,1658,2322,1538,2486,4241,2545,2599,4800,3623,4117,1579,1738,3095,3697,3488,3124,4538,4150,4671,4414,3970,2113,3829,1802,3493,2543,3356,4748,2357,2145,1972,4106,1504,4431,4235,4202,1585,2511,4634,1670,3024,4093,3117,2722,2728,3943,4342,1717,2030,3961,3071,4838,2892,1881,2807,3156,3914,4819,4392,3288,3168,4639,4651,3452,1817,2194,4185,1781,2013,2924,4548,4289,4278,3457,4698,2352,2479,4606,3565,3401,4727,3589,4325,2045,3092,4770,1966,2696,1553,4165,2828,4873,2078,4419,3533,3447,2215,4559,3625,4646,4102,4006,3320,4170,4463,1866,2658,2775,1734,4061,2907,4310,2792,4730,4678,1998,4574,1646,3729,1721,2273,4806,2554,2532,3748,4338,3235,4881,2416,3613,4913,2098,3484,3789,2855,3709,1639,2290,4615,2251,3825,1903,2406,3369,4542,4715,1629,2004,3501,2764,4010,4495,4705,2130,3859,1558,2934,2262,2956,1689,3324,4175,4759,2330,3896,3529,2680,1607,2120,2019,4745,2447,2944,4182,1861,2384,4855,3694,2786,2796,4293,2399,2041,3430,1777,4774,3598,4478,2066,3677,2362,3351,1513,2095,4074,2230,2036,2739,4098,1994,3552,1614,2421,4039,2287,1774,2683,3705,3785,2233,4596,1673,2050,4491,4597,4367,3469,3992,1908,3658,2930,4125,1642,4816,4014,1578,4472,4687,2155,3232,3291,4356,3997,3907,4809,3865,2719,4254,4811,2522,3100,3837,3464,2604,2736,4787,2008,3203,3062,2636,3015,1859,3956,4281,3875,2746,2704,3479,1789,2913,2619,2783,4029,3328,2201,4777,4051,4350,1816,1495,4755,2334,3560,4631,3804,4157,4024,2070,2961,1710,3030,4034,3765,3045,3506,4318,1742,1930,3362,4129,1827,2430,1582,4484,2507,4229,4395,3076,4501,2270,3341,2502,2241,3057,1532,2847,3605,3411,4876,1550,2583,4066,1500,1923,3245,4206,4659,1925,2539,1713,1597,2864,2484,2699,3474,4779,4584,3405,2866,2436,1848,3432,4056,2170,3721,3296,1912,3013,3526,2754,4335,4826,4655,2672,2640,4520,4274,1653,4702,1945,4723,3854,4784,2998,1565,1490,4742,4313,2438,2238,2615,1917,2993,2191,1812,2106,2087,4858,3047,2470,2177,4298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV633-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.27/0.52 % Computer : n007.cluster.edu
% 0.27/0.52 % Model : x86_64 x86_64
% 0.27/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.52 % Memory : 8046.5625MB
% 0.27/0.52 % OS : Linux 6.8.0-71-generic
% 0.27/0.52 % CPULimit : 300
% 0.27/0.52 % WCLimit : 300
% 0.27/0.52 % DateTime : Sat Sep 26 14:37:09 UTC 2026
% 0.27/0.52 % CPUTime :
% 0.27/0.53 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.58/1.45 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.15/2.26 % [INFO] Parsing done (809ms).
% 4.15/2.29 % [INFO] Running in sequential loop mode.
% 5.31/2.91 % [INFO] eprover registered as external prover.
% 5.31/2.92 % [INFO] Scanning for conjecture ...
% 6.64/3.33 % [INFO] Found a conjecture (or negated_conjecture) and 1483 axioms. Running axiom selection ...
% 9.30/3.94 % [INFO] Axiom selection finished. Selected 1481 axioms (removed 2 axioms).
% 11.80/4.60 % [INFO] Problem is propositional (TPTP CNF).
% 11.80/4.66 % [INFO] Type checking passed.
% 11.80/4.67 % [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 ...
% 33.61/10.55 % External prover 'e' found a proof!
% 33.61/10.56 % [INFO] Killing All external provers ...
% 33.61/10.56 % Time passed: 9811ms (effective reasoning time: 8260ms)
% 33.61/10.57 % 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, cls_nat__1__add__1_0, clsarity_Int__Oint__OrderedGroup_Omonoid__add, cls_right__distrib__number__of_0, clsarity_Int__Oint__Ring__and__Field_Osemiring, cls_class__semiring_Osemiring__rules_I20_J_0, cls_zero__le__divide__iff_2, cls_abs__minus__le__zero_0, cls_power__le__zero__eq_3, cls_half__gt__zero_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_divide__less__eq__number__of1_0, cls_divide__less__eq__number__of_1, cls_less__imp__inverse__less__neg_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_add__imp__eq_0, cls_zero__less__power__eq_4, cls_odd__nat__equiv__def_1, cls_divide__le__eq_7, cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_0, cls_frac__le_0, cls_left__distrib__number__of_0, cls_add__le__cancel__right_1, cls_power2__diff_0, cls_div__add__self2_0, cls_mod__add__eq_0, cls_number__of__Pls_0, cls_termination__basic__simps_I1_J_0, cls_divide__less__eq_4, cls_minus__add__distrib_0, cls_zero__less__divide__iff_0, cls_dvd__diff_0, cls_abs__eq__mult_1, 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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
% 33.61/10.57 % No. of inferences in proof: 2965
% 33.61/10.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9811 ms resp. 8260 ms w/o parsing
% 36.00/11.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.00/11.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------