%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV629-1 : 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 : n020.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 09:00:05 AM UTC 2026
% Result : Unsatisfiable 9.70s 3.93s
% Output : Refutation 10.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 389
% Syntax : Number of formulae : 779 ( 227 unt; 0 typ; 0 def)
% Number of atoms : 1717 ( 702 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 7794 ( 842 ~; 938 |; 0 &;6014 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 4 con; 0-3 aty)
% Number of variables : 1672 ( 0 ^;1672 !; 0 ?;1672 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_FFT__Mirabelle_Oroot_decl,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
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_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
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(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_HOL_Oinverse__class_Odivide_decl,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_Complex_Ocnj_decl,type,
c_Complex_Ocnj: $i > $i ).
thf(c_HOL_Oinverse__class_Oinverse_decl,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_HOL_Oabs__class_Oabs_decl,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Odivision__ring_decl,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_Ring__and__Field_Oordered__field_decl,type,
class_Ring__and__Field_Oordered__field: $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_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Ring__and__Field_Odvd_decl,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_decl,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_HOL_Osgn__class_Osgn_decl,type,
c_HOL_Osgn__class_Osgn: $i > $i > $i ).
thf(class_Ring__and__Field_Omult__zero_decl,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add__abs_decl,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $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_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Int_Oiszero_decl,type,
c_Int_Oiszero: $i > $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(class_Nat_Osemiring__char__0_decl,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(class_RealVector_Oreal__normed__div__algebra_decl,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $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_Ring__and__Field_Osgn__if_decl,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_GCD_Ogcd__class_Olcm_decl,type,
c_GCD_Ogcd__class_Olcm: $i > $i > $i > $i ).
thf(c_GCD_Ogcd__class_Ogcd_decl,type,
c_GCD_Ogcd__class_Ogcd: $i > $i > $i > $i ).
thf(c_Parity_Oeven__odd__class_Oeven_decl,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_Fact_Ofact__class_Ofact_decl,type,
c_Fact_Ofact__class_Ofact: $i > $i > $i ).
thf(c_Complex_Oii_decl,type,
c_Complex_Oii: $i ).
thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(260,axiom,
( ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_Complex_Ocnj )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
thf(1036,plain,
( ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_Complex_Ocnj )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(153,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(809,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(85,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(629,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)],[85]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__dvd__mult__iff__nat_1) ).
thf(1190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI2_1) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(32,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(479,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)],[32]) ).
thf(258,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(1031,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)],[258]) ).
thf(386,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(1315,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(216,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(941,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)],[216]) ).
thf(59,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(555,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)],[59]) ).
thf(91,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(645,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)],[91]) ).
thf(194,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(892,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)],[194]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Olcm ) ) @ 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_lcm__semilattice__nat_Ole__sup__iff_1) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Olcm ) ) @ 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)],[282]) ).
thf(226,axiom,
tc_nat @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(962,plain,
tc_nat @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(98,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(666,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)],[98]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI_0) ).
thf(1295,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(307,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(1142,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)],[307]) ).
thf(102,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(677,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)],[102]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj1__iff__nat_1) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(47,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(523,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)],[47]) ).
thf(314,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(1158,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)],[314]) ).
thf(132,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(762,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)],[132]) ).
thf(18,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(440,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)],[18]) ).
thf(43,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(511,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)],[43]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__sup__iff_2) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(179,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(861,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)],[179]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Odistrib__inf__le_0) ).
thf(1078,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(57,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(550,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)],[57]) ).
thf(39,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(500,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)],[39]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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_GCD_Ogcd__class_Ogcd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__mult__distrib__nat_0) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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_GCD_Ogcd__class_Ogcd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq1_0) ).
thf(814,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(358,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(1260,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)],[358]) ).
thf(204,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(913,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)],[204]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divides__mult__nat_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_0) ).
thf(1310,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(51,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(533,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)],[51]) ).
thf(164,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(829,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(333,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(1196,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)],[333]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__commute_0) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(299,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(1127,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)],[299]) ).
thf(232,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__le2_0) ).
thf(973,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(361,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(1265,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(346,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(1228,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)],[346]) ).
thf(93,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(651,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)],[93]) ).
thf(170,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(841,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)],[170]) ).
thf(10,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(417,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)],[10]) ).
thf(378,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(1298,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)],[378]) ).
thf(117,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(719,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)],[117]) ).
thf(150,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__dvd1__nat_0) ).
thf(802,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(385,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_GCD_Ogcd__class_Olcm ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__bot__left_0) ).
thf(1313,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_GCD_Ogcd__class_Olcm ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(213,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(934,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)],[213]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI2_0) ).
thf(853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__least__nat_0) ).
thf(1147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__commute__nat_0) ).
thf(870,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(189,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(881,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)],[189]) ).
thf(21,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(448,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)],[21]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__absorb1_0) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(158,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(817,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)],[158]) ).
thf(199,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__0__left__nat_0) ).
thf(902,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(251,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__dvd2__nat_0) ).
thf(1013,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(135,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__dvd1__nat_0) ).
thf(770,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(209,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__nonzero__nat_0) ).
thf(924,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Fact_Ofact__class_Ofact ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(144,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(789,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)],[144]) ).
thf(19,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(443,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)],[19]) ).
thf(292,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(1109,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)],[292]) ).
thf(44,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(514,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)],[44]) ).
thf(311,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(1151,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)],[311]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI1_1) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(152,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(806,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)],[152]) ).
thf(228,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(966,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_prod__gcd__lcm__nat_0) ).
thf(1051,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(34,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(485,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)],[34]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj2__iff__nat_1) ).
thf(1136,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Oinf__sup__absorb_0) ).
thf(877,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(122,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(734,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)],[122]) ).
thf(23,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(453,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)],[23]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( C
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__common__divisor__nat_0) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( C
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(96,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(660,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)],[96]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__dvd__prod__nat_0) ).
thf(998,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(49,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(527,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)],[49]) ).
thf(4,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(397,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)],[4]) ).
thf(106,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(687,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)],[106]) ).
thf(340,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(1215,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)],[340]) ).
thf(87,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(634,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)],[87]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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__gcd__D1__nat_0) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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)],[290]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( C
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__nat_0) ).
thf(849,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( C
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(276,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__idem__nat_0) ).
thf(1074,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_0) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(207,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(920,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)],[207]) ).
thf(381,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(1306,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(334,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(1199,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)],[334]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI1_0) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(148,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(798,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(269,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(1057,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(317,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(1163,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)],[317]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Olcm ) ) @ 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_lcm__semilattice__nat_Ole__supE_1) ).
thf(910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Olcm ) ) @ 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)],[202]) ).
thf(224,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(957,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)],[224]) ).
thf(126,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(746,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)],[126]) ).
thf(139,axiom,
! [C: $i,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 ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI1_1) ).
thf(778,plain,
! [C: $i,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 ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(356,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(1255,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)],[356]) ).
thf(160,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(820,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)],[160]) ).
thf(61,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(561,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)],[61]) ).
thf(108,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(693,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)],[108]) ).
thf(14,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(429,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)],[14]) ).
thf(350,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(1238,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)],[350]) ).
thf(341,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(1217,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)],[341]) ).
thf(74,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(598,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)],[74]) ).
thf(187,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__unique__nat_4) ).
thf(879,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(174,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(852,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(326,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(1178,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)],[326]) ).
thf(165,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(830,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)],[165]) ).
thf(279,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__num__eq__if__nat_0) ).
thf(1079,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(130,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(757,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)],[130]) ).
thf(24,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(456,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)],[24]) ).
thf(233,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 @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI2_0) ).
thf(974,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 @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(291,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(1106,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)],[291]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( B @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__mult__cancel__nat_0) ).
thf(916,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( B @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(28,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(467,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)],[28]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__greatest_0) ).
thf(847,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(63,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(566,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)],[63]) ).
thf(373,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(1291,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(114,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(710,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)],[114]) ).
thf(67,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(578,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)],[67]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj2__iff__nat_0) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(220,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(948,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)],[220]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq2_0) ).
thf(1017,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(80,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(615,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)],[80]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ c_FFT__Mirabelle_Oroot )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__nonzero_0) ).
thf(1111,plain,
! [A: $i] :
( ( A @ c_FFT__Mirabelle_Oroot )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(119,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(725,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)],[119]) ).
thf(6,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(403,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)],[6]) ).
thf(287,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(1096,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)],[287]) ).
thf(78,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(610,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)],[78]) ).
thf(240,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(989,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(177,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(857,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__mult__nat_0) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(11,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(420,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)],[11]) ).
thf(190,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(884,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)],[190]) ).
thf(315,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(1160,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(35,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(488,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)],[35]) ).
thf(374,axiom,
tc_nat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(1292,plain,
tc_nat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(31,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
thf(476,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(90,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(642,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)],[90]) ).
thf(56,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(547,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)],[56]) ).
thf(257,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(1028,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)],[257]) ).
thf(281,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__ge2_0) ).
thf(1082,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ c_Complex_Ocnj @ c_Complex_Ocnj )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
thf(679,plain,
! [A: $i] :
( ( A @ c_Complex_Ocnj @ c_Complex_Ocnj )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(231,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(970,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)],[231]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Fact_Ofact__class_Ofact ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Nat_Osemiring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__fact__not__zero_0) ).
thf(837,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Fact_Ofact__class_Ofact ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Nat_Osemiring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(288,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(1099,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)],[288]) ).
thf(111,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(701,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)],[111]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_1) ).
thf(1249,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(377,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(1297,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(94,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(654,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)],[94]) ).
thf(271,axiom,
! [A: $i] :
( ( A
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_Complex_Ocnj )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
thf(1060,plain,
! [A: $i] :
( ( A
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_Complex_Ocnj )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__assoc_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(247,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__1__nat_0) ).
thf(1002,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Fact_Ofact__class_Ofact ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(64,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(569,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)],[64]) ).
thf(353,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(1246,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)],[353]) ).
thf(40,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(503,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)],[40]) ).
thf(2,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(393,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)],[2]) ).
thf(294,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 @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI1_0) ).
thf(1114,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 @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(360,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(1263,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)],[360]) ).
thf(244,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__ge1_0) ).
thf(997,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(362,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(1266,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)],[362]) ).
thf(347,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(1231,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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_gcd__semilattice__nat_Ole__infE_0) ).
thf(1318,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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)],[388]) ).
thf(351,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(1241,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)],[351]) ).
thf(42,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(508,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)],[42]) ).
thf(54,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(541,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)],[54]) ).
thf(95,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(657,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)],[95]) ).
thf(321,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(1170,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)],[321]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI_0) ).
thf(1286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(101,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(674,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)],[101]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_GCD_Ogcd__class_Ogcd ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Odistrib__sup__le_0) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_GCD_Ogcd__class_Ogcd ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(50,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(530,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)],[50]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__least_0) ).
thf(888,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(335,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(1202,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)],[335]) ).
thf(146,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(792,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)],[146]) ).
thf(60,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(558,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)],[60]) ).
thf(275,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(1071,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)],[275]) ).
thf(137,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__bot__right_0) ).
thf(773,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(70,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(586,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)],[70]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Complex_Ocnj )
!= ( B @ c_Complex_Ocnj ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Complex_Ocnj )
!= ( B @ c_Complex_Ocnj ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(81,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(618,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)],[81]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( B @ c_GCD_Ogcd__class_Olcm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__left__commute__nat_0) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( B @ c_GCD_Ogcd__class_Olcm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(379,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(1301,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)],[379]) ).
thf(75,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(601,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)],[75]) ).
thf(159,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(819,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__rmult__nat_0) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(12,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(423,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)],[12]) ).
thf(249,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(1007,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)],[249]) ).
thf(298,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__bot__right_0) ).
thf(1125,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(125,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(743,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)],[125]) ).
thf(69,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(584,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)],[69]) ).
thf(312,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__one_0) ).
thf(1154,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(185,axiom,
! [C: $i,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 ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI1_0) ).
thf(875,plain,
! [C: $i,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 ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(162,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(826,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)],[162]) ).
thf(305,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__bot__left_0) ).
thf(1139,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(214,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(936,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)],[214]) ).
thf(65,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(572,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)],[65]) ).
thf(143,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__idem_0) ).
thf(787,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
thf(713,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_2) ).
thf(1058,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(285,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(1090,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)],[285]) ).
thf(206,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(919,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(219,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__unique__nat_3) ).
thf(947,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(344,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(1224,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(357,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(1258,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)],[357]) ).
thf(112,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(704,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)],[112]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__lmult__nat_0) ).
thf(1209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
thf(681,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__commute_0) ).
thf(1282,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Olcm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(265,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(1048,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)],[265]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__assoc__nat_0) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(123,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(737,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)],[123]) ).
thf(297,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(1122,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)],[297]) ).
thf(382,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(1307,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__left__idem_0) ).
thf(863,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(133,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(764,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)],[133]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj2__if__dvd__nat_0) ).
thf(979,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(76,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(604,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)],[76]) ).
thf(198,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__1__nat_0) ).
thf(900,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(7,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(406,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)],[7]) ).
thf(188,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(880,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(263,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(1043,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)],[263]) ).
thf(16,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(434,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)],[16]) ).
thf(193,axiom,
( ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_Complex_Ocnj )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__one_0) ).
thf(890,plain,
( ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_Complex_Ocnj )
= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(37,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(494,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)],[37]) ).
thf(86,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(631,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)],[86]) ).
thf(149,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(799,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)],[149]) ).
thf(82,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(621,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)],[82]) ).
thf(46,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(520,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)],[46]) ).
thf(195,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(895,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__left__idem_0) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(84,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(626,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)],[84]) ).
thf(26,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(462,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)],[26]) ).
thf(178,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(858,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)],[178]) ).
thf(58,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(552,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)],[58]) ).
thf(217,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(943,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(255,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_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__0__iff__nat_0) ).
thf(1022,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_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(375,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_2) ).
thf(1293,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(99,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(668,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)],[99]) ).
thf(88,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(636,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)],[88]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__iff__sup_1) ).
thf(1066,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(140,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(780,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)],[140]) ).
thf(325,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(1176,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)],[325]) ).
thf(238,axiom,
tc_nat @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(986,plain,
tc_nat @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(62,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(563,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)],[62]) ).
thf(289,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(1102,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)],[289]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__greatest__nat_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(203,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(912,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(322,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_3) ).
thf(1171,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
thf(722,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__greatest__iff__nat_2) ).
thf(1034,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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_gcd__semilattice__nat_Ole__inf__iff_1) ).
thf(1304,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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)],[380]) ).
thf(13,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(426,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)],[13]) ).
thf(71,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(589,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)],[71]) ).
thf(218,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(944,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)],[218]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_1) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(97,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(663,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)],[97]) ).
thf(210,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_2) ).
thf(927,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(367,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(1277,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)],[367]) ).
thf(155,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(812,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(215,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(939,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)],[215]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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_gcd__semilattice__nat_Ole__infE_1) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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)],[308]) ).
thf(129,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(754,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)],[129]) ).
thf(30,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(473,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)],[30]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__lcm__I2__nat_0) ).
thf(1076,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ 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_lcm__semilattice__nat_Ole__supE_0) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ 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)],[303]) ).
thf(92,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(648,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)],[92]) ).
thf(280,axiom,
tc_Complex_Ocomplex @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
thf(1081,plain,
tc_Complex_Ocomplex @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(127,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(749,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)],[127]) ).
thf(230,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__top__right_0) ).
thf(968,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(327,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(1181,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)],[327]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__proj2__if__dvd__nat_0) ).
thf(823,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(48,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(525,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)],[48]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__commute__nat_0) ).
thf(855,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( A @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(107,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(690,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)],[107]) ).
thf(256,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(1025,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)],[256]) ).
thf(184,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(872,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)],[184]) ).
thf(8,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(409,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)],[8]) ).
thf(345,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(1225,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)],[345]) ).
thf(113,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(707,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)],[113]) ).
thf(222,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(954,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Parity_Oeven__odd__class_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(355,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__nat_2) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__iff__inf_1) ).
thf(1053,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(329,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(1186,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)],[329]) ).
thf(261,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(1038,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)],[261]) ).
thf(169,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(840,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(221,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(951,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)],[221]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj1__iff__nat_0) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(342,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(1220,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(359,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(1262,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(349,axiom,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__not__zero_0) ).
thf(1235,plain,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(283,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(1085,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)],[283]) ).
thf(29,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(470,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)],[29]) ).
thf(55,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(544,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)],[55]) ).
thf(201,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(907,plain,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(306,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(1141,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(79,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(613,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)],[79]) ).
thf(20,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(446,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)],[20]) ).
thf(73,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(595,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)],[73]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
thf(497,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(343,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(1221,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)],[343]) ).
thf(370,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__0__iff__nat_1) ).
thf(1284,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(27,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(465,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)],[27]) ).
thf(33,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(482,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)],[33]) ).
thf(100,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(671,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)],[100]) ).
thf(313,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_4) ).
thf(1157,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( D @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( C
!= ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( A
!= ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__coprime__nat_0) ).
thf(976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( D @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( C
!= ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( A
!= ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(68,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(581,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)],[68]) ).
thf(131,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(759,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)],[131]) ).
thf(330,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(1189,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(250,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(1010,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)],[250]) ).
thf(171,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(844,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)],[171]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ 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_lcm__semilattice__nat_Ole__sup__iff_0) ).
thf(771,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ 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)],[136]) ).
thf(387,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(1316,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(22,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(450,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)],[22]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj1__if__dvd__nat_0) ).
thf(931,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(53,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(539,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)],[53]) ).
thf(110,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(699,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)],[110]) ).
thf(156,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__dvd2__nat_0) ).
thf(813,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__lcm__I1__nat_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1,negated_conjecture,
( ( 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_conjecture_0) ).
thf(390,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)],[1]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Osup__inf__absorb_0) ).
thf(1244,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(243,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 @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI2_0) ).
thf(995,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 @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(227,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(963,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)],[227]) ).
thf(45,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(517,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)],[45]) ).
thf(121,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn0_0) ).
thf(731,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(142,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__le1_0) ).
thf(786,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(211,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__top__left_0) ).
thf(929,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI1_0) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(332,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(1193,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)],[332]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__nat_1) ).
thf(1212,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(105,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(684,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)],[105]) ).
thf(52,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(536,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)],[52]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__eq__bot__eq2_0) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(116,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(716,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)],[116]) ).
thf(316,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(1161,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)],[316]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__eq__bot__eq1_0) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(302,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(1133,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)],[302]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__dvd__mult__nat_0) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(128,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(752,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)],[128]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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_gcd__semilattice__nat_Ole__inf__iff_0) ).
thf(1280,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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)],[368]) ).
thf(15,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(432,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)],[15]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_5) ).
thf(835,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__left__commute__nat_0) ).
thf(790,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(182,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(867,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)],[182]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__assoc_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_GCD_Ogcd__class_Olcm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(166,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(833,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)],[166]) ).
thf(229,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(967,plain,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(41,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(506,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)],[41]) ).
thf(17,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(437,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)],[17]) ).
thf(268,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(1056,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(163,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(828,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)],[163]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__unique__nat_5) ).
thf(960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Olcm ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(109,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(696,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)],[109]) ).
thf(318,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__0__nat_0) ).
thf(1165,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_GCD_Ogcd__class_Olcm ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Power_Opower__class_Opower ) ) @ c_Complex_Ocnj )
= ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Complex_Ocnj @ c_Power_Opower__class_Opower ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__power_0) ).
thf(955,plain,
! [B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Power_Opower__class_Opower ) ) @ c_Complex_Ocnj )
= ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Complex_Ocnj @ c_Power_Opower__class_Opower ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI2_0) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Olcm ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(323,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(1172,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(134,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(767,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)],[134]) ).
thf(372,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__proj1__if__dvd__nat_0) ).
thf(1288,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(5,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(400,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)],[5]) ).
thf(239,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(987,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)],[239]) ).
thf(300,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(1129,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(25,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(459,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)],[25]) ).
thf(242,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(992,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)],[242]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__mult_0) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(286,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(1093,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)],[286]) ).
thf(3,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(395,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)],[3]) ).
thf(83,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(624,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)],[83]) ).
thf(120,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(728,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)],[120]) ).
thf(124,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(740,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)],[124]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__assoc__nat_0) ).
thf(1268,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) @ c_GCD_Ogcd__class_Ogcd ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__times_0) ).
thf(575,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(236,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(982,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)],[236]) ).
thf(248,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(1004,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)],[248]) ).
thf(151,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(803,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)],[151]) ).
thf(389,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(1320,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(328,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__0__nat_0) ).
thf(1184,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_GCD_Ogcd__class_Ogcd ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(138,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(775,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)],[138]) ).
thf(89,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(639,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)],[89]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI2_1) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_GCD_Ogcd__class_Ogcd ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( B @ c_HOL_Osgn__class_Osgn ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
thf(592,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( B @ c_HOL_Osgn__class_Osgn ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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__gcd__D2__nat_0) ).
thf(1069,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_GCD_Ogcd__class_Ogcd ) ) @ ( 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)],[274]) ).
thf(252,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(1014,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)],[252]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
thf(491,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(284,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(1088,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)],[284]) ).
thf(1329,plain,
$false,
inference(e,[status(thm)],[1036,809,629,1190,1168,479,1031,1315,941,555,645,892,1083,962,666,1295,1142,677,1173,523,1158,762,440,511,1041,861,1078,550,500,1275,814,1260,913,1063,1310,533,829,1196,898,1127,973,1265,1228,651,841,417,1298,719,802,1313,934,853,1147,870,881,448,1232,817,902,1013,770,924,789,443,1109,514,1151,1020,806,966,1051,485,1136,877,734,453,1119,660,998,527,397,687,1215,634,1104,849,1074,1206,920,1306,1199,810,798,1057,1163,910,957,746,778,1255,820,561,693,429,1238,1217,598,879,852,1178,830,1079,757,456,974,1106,916,467,847,566,1291,710,578,1270,948,1017,615,1111,725,403,1096,610,989,857,783,420,884,1160,488,1292,476,642,547,1028,1082,679,970,837,1099,701,1249,1297,654,1060,984,1002,569,1246,503,393,1114,1263,997,1266,1231,1318,1241,508,541,657,1170,1286,674,1167,530,888,1202,792,558,1071,773,586,412,618,1273,1301,601,819,904,423,1007,1125,743,584,1154,875,826,1139,936,572,787,713,1058,1090,919,947,1224,1258,704,1209,681,1282,1048,990,737,1122,1307,863,764,979,604,900,406,880,1043,434,890,494,631,799,621,520,895,1149,626,462,858,552,943,1022,1293,668,636,1066,780,1176,986,563,1102,922,912,1171,722,1034,1304,426,589,944,795,663,927,1277,812,939,1145,754,473,1076,1134,648,1081,749,968,1181,823,525,855,690,1025,872,409,1225,707,954,1252,1053,1186,1038,840,951,1130,1220,1262,1235,1085,470,544,907,1141,613,446,595,497,1221,1284,465,482,671,1157,976,581,759,1189,1010,844,771,1316,450,931,539,699,813,896,390,1244,995,963,517,731,786,929,1308,1193,1212,684,536,1045,716,1161,1116,1133,999,752,1280,432,835,790,867,865,833,967,506,437,1056,828,960,696,1165,955,886,1172,767,1288,400,987,1129,459,992,607,1093,395,624,728,740,1268,575,982,1004,803,1320,1184,775,639,1204,592,1069,1014,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV629-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 14:39:49 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.93/1.30 % [INFO] Parsing done (331ms).
% 1.93/1.31 % [INFO] Running in sequential loop mode.
% 2.50/1.69 % [INFO] eprover registered as external prover.
% 2.50/1.69 % [INFO] Scanning for conjecture ...
% 2.89/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 388 axioms. Running axiom selection ...
% 3.09/1.99 % [INFO] Axiom selection finished. Selected 388 axioms (removed 0 axioms).
% 4.37/2.20 % [INFO] Problem is propositional (TPTP CNF).
% 4.37/2.22 % [INFO] Type checking passed.
% 4.37/2.23 % [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 ...
% 9.70/3.92 % External prover 'e' found a proof!
% 9.70/3.92 % [INFO] Killing All external provers ...
% 9.70/3.92 % Time passed: 3390ms (effective reasoning time: 2602ms)
% 9.70/3.93 % Axioms used in derivation (388): cls_gcd__semilattice__nat_Oless__infI2_1, cls_gcd__greatest__nat_0, cls_power__0_0, cls_gcd__lcm__complete__lattice__nat_Osup__eq__bot__eq1_0, cls_divide__eq__eq_3, cls_gcd__proj1__if__dvd__nat_0, cls_mult__cancel2_0, cls_mult__zero__right_0, cls_nat__dvd__1__iff__1_1, cls_dvd_Oantisym__conv_0, cls_lcm__semilattice__nat_Osup__idem_0, cls_nat__mult__eq__1__iff_1, cls_dvd__mult2_0, cls_of__nat__0_0, cls_even__zero__nat_0, cls_gcd__unique__nat_5, cls_gcd__lcm__lattice__nat_Osup__inf__absorb_0, cls_mult__right_Ozero_0, cls_dvd__mult__right_0, cls_gcd__zero__nat_1, cls_lcm__semilattice__nat_Osup__commute_0, cls_gcd__0__nat_0, cls_lcm__left__commute__nat_0, cls_not__iszero__1_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_gcd__mult__distrib__nat_0, cls_inverse__zero__imp__zero_0, cls_divide__self_0, cls_gcd__lcm__complete__lattice__nat_Osup__bot__left_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_sgn__times_0, cls_nat__1__eq__mult__iff_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_gcd__dvd2__nat_0, cls_mult__is__0_2, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_gcd__semilattice__nat_Oless__infI1_1, cls_power__eq__0__iff_1, cls_inverse__eq__iff__eq_0, cls_divide__1_0, cls_gcd__semilattice__nat_Ole__infI_0, cls_gcd__semilattice__nat_Ole__infI2_0, cls_coprime__common__divisor__nat_0, cls_complex__cnj__one_0, cls_nonzero__inverse__eq__divide_0, cls_sgn0_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1, cls_divides__mult__nat_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_abs__dvd__iff_1, cls_gcd__semilattice__nat_Ole__infE_1, cls_dvd__div__mult__self_0, cls_inverse__1_0, cls_abs__of__nat_0, cls_lcm__semilattice__nat_Osup__ge1_0, cls_divide__eq__eq_0, cls_power__one_0, cls_left__inverse_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_gcd__semilattice__nat_Oinf__commute_0, cls_coprime__nat_2, cls_nat__mult__1_0, cls_lcm__dvd1__nat_0, cls_div__by__0_0, cls_gcd__semilattice__nat_Ole__inf__iff_0, cls_sgn__zero_0, cls_lcm__commute__nat_0, cls_inverse__divide_0, cls_mult__eq__0__iff_0, cls_complex__cnj__cancel__iff_0, cls_even__product__nat_1, cls_gcd__lcm__complete__lattice__nat_Osup__top__left_0, cls_eq__divide__eq_4, clsarity_nat__Ring__and__Field_Osemiring__0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_frac__eq__eq_0, cls_lcm__proj2__if__dvd__nat_0, clsarity_nat__Divides_Osemiring__div, cls_divide__eq__eq_4, clsarity_nat__OrderedGroup_Omonoid__mult, cls_fact__nonzero__nat_0, cls_dvd__lcm__I1__nat_0, cls_power__even__abs_0, cls_mult_Ozero__left_0, cls_gcd__commute__nat_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_field__power__not__zero_0, cls_lcm__semilattice__nat_Ole__sup__iff_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_lcm__semilattice__nat_Osup__absorb1_0, cls_div__mult__self2__is__id_0, cls_power__0__left_0, cls_mult_Ozero__right_0, cls_class__semiring_Omul__c_0, cls_inverse__eq__1__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, cls_mult__dvd__mono_0, cls_div__self_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_div__mult__mult1_0, cls_class__fieldgb_Oinverse__divide_0, cls_gcd__lcm__complete__lattice__nat_Osup__top__right_0, cls_gcd__proj2__if__dvd__nat_0, cls_dvd__mult__cancel__right_2, cls_gcd__lcm__complete__lattice__nat_Oinf__bot__right_0, cls_inverse__nonzero__iff__nonzero_0, cls_gcd__zero__nat_0, cls_dvd__mult__div__cancel_0, cls_lcm__semilattice__nat_Ole__supE_0, cls_lcm__semilattice__nat_Osup__assoc_0, cls_power__one__over_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_nonzero__abs__inverse_0, cls_mult__sgn__abs_0, cls_mult__is__0_1, cls_dvd_Oless__le__trans_1, cls_root0_0, cls_gcd__semilattice__nat_Oless__infI2_0, cls_no__zero__divisors_0, cls_cnj_Ozero_0, cls_div__mult__div__if__dvd_0, cls_mult__frac__num_0, cls_lcm__semilattice__nat_Ole__sup__iff_2, cls_mult__frac__frac_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_lcm__0__iff__nat_1, cls_mult__1__right_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_gcd__unique__nat_4, cls_sgn__0__0_0, cls_nat__mult__dvd__cancel__disj_0, cls_of__nat__1_0, cls_nat__mult__1__right_0, cls_gcd__greatest__iff__nat_2, cls_power__eq__0__iff_2, cls_class__semiring_Osemiring__rules_I15_J_0, cls_dvd__trans_0, cls_gcd__semilattice__nat_Ole__infE_0, cls_complex__i__not__zero_0, cls_abs__eq__0_0, cls_lcm__1__iff__nat_1, clsarity_Complex__Ocomplex__Nat_Osemiring__char__0, cls_power__mult_0, cls_sgn__0__0_1, cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq1_0, cls_eq__divide__eq_0, cls_dvd_Oeq__iff_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, cls_divide__self__if_1, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_eq__divide__eq_3, cls_of__nat__eq__iff_0, cls_gcd__assoc__nat_0, cls_class__semiring_Osemiring__rules_I17_J_0, clsarity_nat__Nat_Osemiring__char__0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, cls_class__semiring_Osemiring__rules_I19_J_0, cls_fact__num__eq__if__nat_0, cls_gcd__semilattice__nat_Ole__inf__iff_1, cls_lcm__semilattice__nat_Ole__iff__sup_1, cls_divide_Ozero_0, cls_divide__self__if_0, cls_dvd__abs__iff_0, cls_abs__idempotent_0, cls_gcd__left__commute__nat_0, cls_dvd__antisym_0, cls_dvd__triv__right_0, cls_lcm__unique__nat_3, cls_dvd_Oless__le__trans_0, cls_lcm__proj2__iff__nat_1, cls_fact__1__nat_0, cls_dvd__div__mult_0, cls_gcd__semilattice__nat_Oinf__le1_0, cls_gcd__semilattice__nat_Oinf__assoc_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_lcm__semilattice__nat_Osup__left__idem_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, cls_nat__1__eq__mult__iff_2, cls_power__divide_0, cls_even__product__nat_2, cls_power__abs_0, cls_sgn__zero__iff_0, cls_coprime__lmult__nat_0, cls_dvd__lcm__I2__nat_0, cls_gcd__lcm__lattice__nat_Oinf__sup__absorb_0, cls_of__nat__mult_0, cls_lcm__least__nat_0, cls_gcd__semilattice__nat_Oinf__greatest_0, cls_div__by__1_0, cls_dvd__if__abs__eq_0, cls_no__zero__divirors__neq0_0, cls_gcd__semilattice__nat_Ole__iff__inf_1, cls_inverse__nonzero__iff__nonzero_1, cls_dvd__mult__cancel__left_2, cls_coprime__nat_0, cls_zero__neq__one_0, cls_dvd__refl_0, cls_inverse__eq__1__iff_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring, cls_dvd__mult__cancel__right_1, cls_nat__mult__dvd__cancel__disj_1, cls_lcm__semilattice__nat_Ole__supI1_0, cls_lcm__semilattice__nat_Ole__supE_1, cls_lcm__semilattice__nat_Osup__ge2_0, cls_gcd__lcm__complete__lattice__nat_Oinf__bot__left_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one, cls_mult__is__0_0, cls_dvd__gcd__D2__nat_0, cls_lcm__semilattice__nat_Oless__supI1_0, cls_dvd_Oless__trans_1, cls_divide__zero_0, cls_right__inverse_0, cls_class__semiring_Omul__a_0, cls_power__inverse_0, cls_class__semiring_Omul__1_0, clsarity_nat__Ring__and__Field_Odvd, cls_gcd__unique__nat_3, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, cls_inverse__unique_0, cls_gcd__semilattice__nat_Ole__inf__iff_2, cls_gcd__lcm__complete__lattice__nat_Osup__eq__bot__eq2_0, cls_complex__i__not__one_0, clsarity_nat__OrderedGroup_Oab__semigroup__mult, cls_div__dvd__div_0, cls_dvd_Oless__le_0, cls_abs__dvd__iff_0, cls_dvd__gcd__D1__nat_0, cls_mult__eq__0__iff_2, cls_mult__cancel1_1, cls_nonzero__abs__divide_0, cls_divide__zero__left_0, cls_class__semiring_Opwr__pwr_0, cls_lcm__semilattice__nat_Osup__least_0, cls_dvd__triv__left_0, cls_coprime__dvd__mult__nat_0, cls_nat__1__eq__mult__iff_1, cls_eq__divide__eq_2, cls_lcm__1__iff__nat_0, cls_gcd__mult__cancel__nat_0, cls_abs__mult__self_0, cls_dvd__power_1, cls_one__dvd_0, cls_div__0_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odvd, cls_nat__mult__eq__1__iff_2, cls_gcd__semilattice__nat_Oinf__left__idem_0, cls_lcm__0__nat_0, cls_lcm__unique__nat_5, clsarity_nat__Power_Opower, cls_gcd__dvd1__nat_0, cls_nonzero__inverse__inverse__eq_0, cls_power__mult__distrib_0, cls_dvd_Ole__less__trans_1, cls_eq__divide__imp_0, cls_class__semiring_Osemiring__rules_I11_J_0, cls_lcm__assoc__nat_0, cls_lcm__proj2__iff__nat_0, cls_lcm__semilattice__nat_Oless__supI2_0, cls_abs__divide_0, cls_one__neq__zero_0, cls_lcm__proj1__iff__nat_1, cls_nonzero__inverse__eq__imp__eq_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, cls_divide__eq__imp_0, cls_complex__cnj__zero__iff_0, cls_power__commutes_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_dvd__mult__cancel__left_1, cls_root__nonzero_0, cls_iszero__def_0, cls_gcd__semilattice__nat_Oinf__le2_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_coprime__dvd__mult__iff__nat_1, cls_dvd_Ole__neq__trans_0, cls_inverse__inverse__eq_0, cls_gcd__idem__nat_0, cls_coprime__rmult__nat_0, cls_mult__1_0, cls_dvd__abs__iff_1, cls_dvd__mult__left_0, cls_lcm__unique__nat_4, cls_abs__mult_0, cls_sgn__sgn_0, cls_lcm__semilattice__nat_Ole__supI2_0, cls_div__power_0, cls_coprime__mult__nat_0, cls_prod__gcd__lcm__nat_0, cls_gcd__0__left__nat_0, cls_power__one__right_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors, cls_mult__1__left_0, cls_gcd__zero__nat_2, cls_frac__eq__eq_1, cls_mult__zero__left_0, cls_dvd_Oeq__iff_2, cls_dvd__mult__cancel__right_0, cls_nat__mult__eq__1__iff_0, cls_div__mult__mult2_0, cls_dvd_Oless__trans_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field, cls_dvd_Oorder__trans_0, cls_power__eq__0__iff_0, cls_dvd__0__right_0, cls_complex__cnj__cnj_0, cls_dvd_Oneq__le__trans_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_class__fieldgb_Odivide__inverse_0, cls_abs__sgn_0, cls_nonzero__power__divide_0, cls_inverse__zero_0, cls_nat__mult__dvd__cancel__disj_2, cls_dvd_Oantisym_0, cls_sgn__one_0, cls_complex__cnj__power_0, cls_gcd__lcm__lattice__nat_Odistrib__sup__le_0, cls_sgn__mult_0, cls_inverse__eq__divide_0, cls_root__unity_0, clsarity_Complex__Ocomplex__Power_Opower, cls_mult__divide__mult__cancel__right_0, cls_class__semiring_Opwr__mul_0, cls_odd__1__nat_0, cls_of__nat__fact__not__zero_0, cls_lcm__proj1__iff__nat_0, cls_lcm__1__iff__nat_2, cls_abs__inverse_0, cls_gcd__1__nat_0, cls_gcd__lcm__lattice__nat_Odistrib__inf__le_0, cls_nat__mult__assoc_0, cls_gcd__semilattice__nat_Oless__infI1_0, cls_dvdI_0, cls_divide__inverse_0, cls_field__inverse_0, cls_abs__eq__0_1, cls_nat__mult__commute_0, cls_gcd__lcm__complete__lattice__nat_Obot__least_0, cls_gcd__lcm__complete__lattice__nat_Osup__bot__right_0, cls_abs__one_0, cls_div__dvd__div_1, cls_lcm__semilattice__nat_Ole__sup__iff_1, cls_mult__eq__self__implies__10_0, cls_inverse__mult__distrib_0, cls_class__semiring_Opwr__0_0, cls_mult__eq__0__iff_1, cls_gcd__semilattice__nat_Ole__infI1_0, cls_mult__cancel1_0, cls_lcm__0__iff__nat_0, cls_lcm__semilattice__nat_Oless__supI2_1, 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_div__mult__self1__is__id_0, cls_mult__idem_0, cls_dvd__mult_0, cls_gcd__coprime__nat_0, cls_divide__eq__eq_1, cls_nat__dvd__1__iff__1_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq2_0, cls_div__mult__mult1__if_0, cls_lcm__semilattice__nat_Ole__supI_0, cls_lcm__proj1__if__dvd__nat_0, cls_nat__mult__eq__cancel__disj_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_lcm__semilattice__nat_Oless__supI1_1, cls_dvd_Ole__less__trans_0, cls_lcm__dvd2__nat_0, cls_mult__divide__mult__cancel__left_0, cls_mult__left_Ozero_0, cls_gcd__dvd__prod__nat_0, cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0, cls_coprime__nat_1, cls_power__0__left_1, cls_iszero__0_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, cls_right__inverse__eq_1, cls_dvd__0__left_0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1
% 9.70/3.93 % No. of inferences in proof: 779
% 9.70/3.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3390 ms resp. 2602 ms w/o parsing
% 10.69/4.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.69/4.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------