TSTP Solution File: SWV629-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV629-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:17:38 EDT 2023
% Result : Unsatisfiable 7.31s 2.67s
% Output : Refutation 8.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 440
% Syntax : Number of formulae : 830 ( 227 unt; 51 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 : 69 ( 69 >; 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_type,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_Complex_Ocnj_type,type,
c_Complex_Ocnj: $i > $i ).
thf(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_HOL_Oabs__class_Oabs_type,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_Ring__and__Field_Oordered__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Ring__and__Field_Odvd_type,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_HOL_Osgn__class_Osgn_type,type,
c_HOL_Osgn__class_Osgn: $i > $i > $i ).
thf(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add__abs_type,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Int_Oiszero_type,type,
c_Int_Oiszero: $i > $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(class_RealVector_Oreal__normed__div__algebra_type,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Osgn__if_type,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_GCD_Ogcd__class_Olcm_type,type,
c_GCD_Ogcd__class_Olcm: $i > $i > $i > $i ).
thf(c_GCD_Ogcd__class_Ogcd_type,type,
c_GCD_Ogcd__class_Ogcd: $i > $i > $i > $i ).
thf(c_Parity_Oeven__odd__class_Oeven_type,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_Fact_Ofact__class_Ofact_type,type,
c_Fact_Ofact__class_Ofact: $i > $i > $i ).
thf(c_Complex_Oii_type,type,
c_Complex_Oii: $i ).
thf(class_RealVector_Oreal__normed__algebra__1_type,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI1_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(1024,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(1105,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(387,axiom,
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__1__nat_0) ).
thf(1315,plain,
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(962,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI1_1) ).
thf(777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(293,axiom,
! [A: $i] :
( ( c_FFT__Mirabelle_Oroot @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__nonzero_0) ).
thf(1110,plain,
! [A: $i] :
( ( c_FFT__Mirabelle_Oroot @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
thf(481,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
thf(1237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__greatest_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supE_1) ).
thf(909,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__nat_1) ).
thf(1211,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
= ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(683,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
= ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__gcd__D2__nat_0) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI2_0) ).
thf(994,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(276,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__idem__nat_0) ).
thf(1073,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= B )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj2__iff__nat_0) ).
thf(1269,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= B )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(187,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__unique__nat_4) ).
thf(878,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(614,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(121,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn0_0) ).
thf(730,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(373,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(1290,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_0) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(449,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(381,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(1305,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= C )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= C )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(279,axiom,
( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__num__eq__if__nat_0) ).
thf(1078,plain,
( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(715,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(472,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
thf(698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(538,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj1__if__dvd__nat_0) ).
thf(930,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(100,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(670,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(318,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__0__nat_0) ).
thf(1164,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(148,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(797,plain,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(247,axiom,
( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__1__nat_0) ).
thf(1001,plain,
( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Osup__inf__absorb_0) ).
thf(1243,plain,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ A @ C @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__mult__nat_0) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ A @ C @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__divide_0) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
thf(1265,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(829,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
thf(1095,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI2_0) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI2_0) ).
thf(885,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(372,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__proj1__if__dvd__nat_0) ).
thf(1287,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(142,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__le1_0) ).
thf(785,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(361,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(1264,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(802,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_0) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(268,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(1055,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(724,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(271,axiom,
! [A: $i] :
( ( ( c_Complex_Ocnj @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
thf(1059,plain,
! [A: $i] :
( ( ( c_Complex_Ocnj @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(302,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).
thf(1132,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
thf(638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(1087,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(389,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(1319,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(416,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__eq__bot__eq1_0) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).
thf(969,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__mult_0) ).
thf(606,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(252,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
thf(1013,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__sup__iff_0) ).
thf(770,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(31,axiom,
! [A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
thf(475,plain,
! [A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(756,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ B @ ( c_GCD_Ogcd__class_Ogcd @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__left__commute__nat_0) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ B @ ( c_GCD_Ogcd__class_Ogcd @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
= ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
thf(591,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
= ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__sup__iff_2) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_5) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__times_0) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(229,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(966,plain,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(328,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__0__nat_0) ).
thf(1183,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(370,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__0__iff__nat_1) ).
thf(1283,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
thf(956,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(774,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__dvd__mult__nat_0) ).
thf(998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(240,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(988,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(42,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ E @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ E @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
thf(507,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ E @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ E @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).
thf(981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(321,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).
thf(1169,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(428,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(335,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(103,axiom,
! [A: $i] :
( ( c_Complex_Ocnj @ ( c_Complex_Ocnj @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
thf(678,plain,
! [A: $i] :
( ( c_Complex_Ocnj @ ( c_Complex_Ocnj @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(529,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(546,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(382,axiom,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(1306,plain,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(217,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(942,plain,
class_Power_Opower @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(439,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(312,axiom,
! [A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra__1 @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__one_0) ).
thf(1153,plain,
! [A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra__1 @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(798,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_2) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__mult__distrib__nat_0) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(162,axiom,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root0_0) ).
thf(825,plain,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__0__iff__nat_0) ).
thf(1021,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(263,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
thf(1042,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__left__idem_0) ).
thf(862,plain,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
thf(630,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(144,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Obot__least_0) ).
thf(788,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(344,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(1223,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(195,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
thf(894,plain,
class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(484,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A )
= C )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A )
= C )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(188,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(879,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI2_0) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(193,axiom,
( ( c_Complex_Ocnj @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__one_0) ).
thf(889,plain,
( ( c_Complex_Ocnj @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(257,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1027,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(333,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
thf(1195,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__commute_0) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(374,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(1291,plain,
class_Divides_Osemiring__div @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(251,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__dvd2__nat_0) ).
thf(1012,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(377,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(1296,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(665,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(69,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__0_0) ).
thf(583,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(315,axiom,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(1159,plain,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(26,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(461,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Int_Oiszero @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__def_0) ).
thf(551,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Int_Oiszero @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(300,axiom,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(1128,plain,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI1_0) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).
thf(1259,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(1227,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(305,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__bot__left_0) ).
thf(1138,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__commute__nat_0) ).
thf(869,plain,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( C
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__common__divisor__nat_0) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( C
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(499,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__assoc__nat_0) ).
thf(989,plain,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(178,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(857,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Oabs__class_Oabs @ C @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
thf(519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Oabs__class_Oabs @ C @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(742,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(349,axiom,
( c_Complex_Oii
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__not__zero_0) ).
thf(1234,plain,
( c_Complex_Oii
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__sup__iff_1) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq2_0) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(706,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(375,axiom,
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_2) ).
thf(1292,plain,
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
thf(933,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(554,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(199,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__0__left__nat_0) ).
thf(901,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__lcm__I2__nat_0) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
thf(393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(238,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(985,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__absorb1_0) ).
thf(1231,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_prod__gcd__lcm__nat_0) ).
thf(1050,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(203,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
thf(911,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
thf(721,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_Power_Opower__class_Opower @ B @ C @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__even__abs_0) ).
thf(779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_Power_Opower__class_Opower @ B @ C @ A ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__dvd__prod__nat_0) ).
thf(997,plain,
! [C: $i,B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(215,axiom,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ A ) @ A @ tc_Complex_Ocomplex )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
thf(938,plain,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ A ) @ A @ tc_Complex_Ocomplex )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
thf(805,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__greatest__nat_0) ).
thf(921,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(322,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_3) ).
thf(1170,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(260,axiom,
( ( c_Complex_Ocnj @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
thf(1035,plain,
( ( c_Complex_Ocnj @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI2_1) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_1) ).
thf(794,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(210,axiom,
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_2) ).
thf(926,plain,
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(222,axiom,
c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
thf(953,plain,
c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(662,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(718,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(201,axiom,
( c_Complex_Oii
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__not__one_0) ).
thf(906,plain,
( c_Complex_Oii
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(228,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(965,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(355,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__nat_2) ).
thf(1251,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
thf(425,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__gcd__D1__nat_0) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(342,axiom,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(1219,plain,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(177,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(856,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(733,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj2__iff__nat_1) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ( c_Complex_Ocnj @ A )
!= ( c_Complex_Ocnj @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( ( c_Complex_Ocnj @ A )
!= ( c_Complex_Ocnj @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(513,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__least__nat_0) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(819,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(171,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(843,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(137,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__bot__right_0) ).
thf(772,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(298,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__bot__right_0) ).
thf(1124,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ B @ ( c_GCD_Ogcd__class_Ogcd @ C @ A @ tc_nat ) @ tc_nat ) )
| ( C
!= ( c_HOL_Otimes__class_Otimes @ D @ ( c_GCD_Ogcd__class_Ogcd @ C @ A @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ C @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ D @ B @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__coprime__nat_0) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ B @ ( c_GCD_Ogcd__class_Ogcd @ C @ A @ tc_nat ) @ tc_nat ) )
| ( C
!= ( c_HOL_Otimes__class_Otimes @ D @ ( c_GCD_Ogcd__class_Ogcd @ C @ A @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ C @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ D @ B @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(641,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(385,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__bot__left_0) ).
thf(1312,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(207,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(919,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(220,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).
thf(947,plain,
! [A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).
thf(1224,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(466,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(1092,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(736,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(244,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__ge1_0) ).
thf(996,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infE_1) ).
thf(1144,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(880,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI1_0) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
thf(1175,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(155,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(811,plain,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(280,axiom,
class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
thf(1080,plain,
class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(535,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(816,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).
thf(1162,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__lcm__I1__nat_0) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ C @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__mult__cancel__nat_0) ).
thf(915,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ C @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(135,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__dvd1__nat_0) ).
thf(769,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
thf(943,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(326,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(1177,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( C
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__nat_0) ).
thf(848,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( C
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(700,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__assoc_0) ).
thf(983,plain,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(334,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1198,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__unique__nat_5) ).
thf(959,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(163,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).
thf(827,plain,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(239,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
thf(986,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI1_0) ).
thf(1113,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(174,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(851,plain,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(431,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
thf(653,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(323,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(1171,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__eq__bot__eq2_0) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(353,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(1245,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(883,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(36,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
thf(490,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ A @ C @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Odistrib__sup__le_0) ).
thf(1166,plain,
! [C: $i,B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ A @ C @ tc_nat ) @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
thf(680,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(487,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(156,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__dvd2__nat_0) ).
thf(812,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(281,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__ge2_0) ).
thf(1081,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__power_0) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ B @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__fact__not__zero_0) ).
thf(836,plain,
! [B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ B @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI2_1) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__lmult__nat_0) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(617,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(1070,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(313,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_4) ).
thf(1156,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__least_0) ).
thf(887,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ A @ B @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ A ) @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__power_0) ).
thf(954,plain,
! [B: $i,A: $i] :
( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ A @ B @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ A ) @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__assoc__nat_0) ).
thf(1267,plain,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
thf(712,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
thf(557,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(1003,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(409,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(347,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(1230,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).
thf(1300,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(791,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(330,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(1188,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(585,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(840,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).
thf(1262,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infE_0) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(153,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(808,plain,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI_0) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(343,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(1220,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(357,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(1257,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(307,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(1141,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(656,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(600,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__iff__inf_1) ).
thf(1052,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__assoc_0) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(120,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(727,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(571,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Oinf__sup__absorb_0) ).
thf(876,plain,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj2__if__dvd__nat_0) ).
thf(978,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(306,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(1140,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ B @ ( c_GCD_Ogcd__class_Olcm @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__left__commute__nat_0) ).
thf(1272,plain,
! [C: $i,B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ B @ ( c_GCD_Ogcd__class_Olcm @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(1240,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(1084,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(1180,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(314,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
thf(1157,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ A @ C @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__rmult__nat_0) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ A @ C @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
thf(524,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).
thf(1126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coprime__dvd__mult__iff__nat_1) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(341,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(1216,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).
thf(891,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(588,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(748,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divides__mult__nat_0) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1,negated_conjecture,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(390,plain,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(143,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__idem_0) ).
thf(786,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(226,axiom,
class_Ring__and__Field_Odvd @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(961,plain,
class_Ring__and__Field_Odvd @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq1_0) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(219,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__unique__nat_3) ).
thf(946,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(64,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(568,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(763,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(198,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__1__nat_0) ).
thf(899,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
thf(832,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ B @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_0) ).
thf(1309,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(667,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI_0) ).
thf(1294,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ A @ C @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Odistrib__inf__le_0) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ A @ C @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ A @ ( c_GCD_Ogcd__class_Olcm @ B @ C @ tc_nat ) @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supE_0) ).
thf(1133,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(620,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
thf(447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(230,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__top__right_0) ).
thf(967,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).
thf(950,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(159,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(818,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__left__idem_0) ).
thf(1148,plain,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ A @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(603,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__commute__nat_0) ).
thf(854,plain,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_1) ).
thf(1303,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_1) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(386,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(1314,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(269,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(1056,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(164,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(828,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(635,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(211,axiom,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__top__left_0) ).
thf(928,plain,
! [A: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(206,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(918,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(150,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__dvd1__nat_0) ).
thf(801,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj1__iff__nat_1) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
= A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__commute_0) ).
thf(897,plain,
! [B: $i,A: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__greatest__iff__nat_2) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_GCD_Ogcd__class_Ogcd @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(400,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(532,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= B )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__iff__sup_1) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= B )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__proj1__iff__nat_0) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat )
!= A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(359,axiom,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(1261,plain,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(179,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).
thf(860,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI1_1) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
thf(644,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__proj2__if__dvd__nat_0) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(871,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(3,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(395,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(169,axiom,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(839,plain,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(209,axiom,
! [A: $i] :
( ( c_Fact_Ofact__class_Ofact @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__nonzero__nat_0) ).
thf(923,plain,
! [A: $i] :
( ( c_Fact_Ofact__class_Ofact @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(659,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(543,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
thf(496,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(232,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__le2_0) ).
thf(972,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(469,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(216,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
thf(940,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(935,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(1009,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(1037,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1320,plain,
$false,
inference(e,[status(thm)],[809,1024,1105,1315,962,777,1110,481,1237,846,909,628,1211,683,1068,994,1073,1269,878,614,730,1290,1205,449,1305,597,1078,715,472,698,538,930,670,1164,797,1001,1243,782,709,565,436,1265,1254,829,1095,973,885,1287,785,1264,751,802,1279,1055,724,1059,1132,638,1087,1319,416,1115,969,606,1013,770,475,756,789,591,1040,623,834,574,966,1183,1283,692,956,866,774,998,988,507,981,766,1169,397,428,1201,452,678,529,546,1306,942,439,1153,761,1047,798,1057,1274,825,1021,1042,862,630,788,1223,894,484,625,879,852,889,493,1027,1195,1281,1291,1012,1296,665,583,522,1159,461,551,1128,874,1259,650,1121,1227,403,1006,1138,869,1118,499,989,857,519,742,1089,1234,1160,1082,526,1214,1016,706,1292,933,554,753,901,686,1075,393,985,1150,1297,1231,1192,1050,911,721,779,647,997,938,633,805,921,1170,1035,1167,794,926,953,1185,662,718,906,965,1251,425,1103,1219,856,745,689,733,1135,412,513,1146,819,843,772,577,1124,562,975,641,445,1312,919,947,1224,540,466,1092,406,419,736,996,1144,880,1307,1175,811,1080,758,535,816,609,594,1162,895,915,769,943,1177,848,700,983,1198,959,827,986,1113,851,505,431,653,912,1171,1044,695,1245,455,883,490,1166,680,487,812,1081,458,836,1203,1208,617,516,580,1070,1156,887,954,739,1267,1098,712,557,1003,409,1230,673,1300,791,1188,585,502,840,1262,1317,808,1285,1220,1257,703,1141,656,600,1052,864,727,571,876,978,1140,1272,612,1240,991,1084,1180,1157,903,524,1126,1189,1108,1216,891,1276,588,748,1062,390,786,961,813,946,1101,1030,568,763,899,832,1309,549,433,510,667,1294,1077,478,1133,620,447,967,950,818,1148,603,854,1303,422,1248,1314,1056,828,635,928,918,801,1172,897,1033,400,532,1065,464,1129,1261,860,1019,644,822,442,871,395,839,923,659,543,676,496,972,469,940,935,1009,1037,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV629-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:59:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.89/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.63/1.05 % [INFO] Parsing done (212ms).
% 1.63/1.06 % [INFO] Running in sequential loop mode.
% 2.20/1.26 % [INFO] eprover registered as external prover.
% 2.20/1.26 % [INFO] cvc4 registered as external prover.
% 2.20/1.26 % [INFO] Scanning for conjecture ...
% 2.44/1.35 % [INFO] Found a conjecture and 388 axioms. Running axiom selection ...
% 2.60/1.44 % [INFO] Axiom selection finished. Selected 388 axioms (removed 0 axioms).
% 3.25/1.57 % [INFO] Problem is propositional (TPTP CNF).
% 3.25/1.58 % [INFO] Type checking passed.
% 3.25/1.58 % [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 ...
% 7.31/2.67 % External prover 'e' found a proof!
% 7.31/2.67 % [INFO] Killing All external provers ...
% 7.31/2.67 % Time passed: 2157ms (effective reasoning time: 1608ms)
% 7.31/2.67 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.31/2.67 % 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
% 7.31/2.67 % No. of inferences in proof: 779
% 7.31/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2157 ms resp. 1608 ms w/o parsing
% 8.33/2.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.33/2.82 % [INFO] Killing All external provers ...
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