TSTP Solution File: SWW189+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW189+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 12:21:52 EDT 2023
% Result : Timeout 298.78s 60.72s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1141
% Syntax : Number of formulae : 2324 ( 353 unt; 113 typ; 0 def)
% Number of atoms : 6566 (2105 equ; 0 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 32012 ( 751 ~; 423 |; 565 &;26924 @)
% ( 220 <=>;3129 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% Number of symbols : 116 ( 113 usr; 6 con; 0-5 aty)
% Number of variables : 5672 ( 0 ^;5625 !; 47 ?;5672 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(v_p_type,type,
v_p: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(v_a_type,type,
v_a: $i ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
thf(c_Polynomial_Opos__poly_type,type,
c_Polynomial_Opos__poly: $i > $i > $o ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Rings_Odvd__class_Odvd_type,type,
c_Rings_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(c_Polynomial_Opdivmod__rel_type,type,
c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_Rings_Oordered__cancel__semiring_type,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
thf(c_Rings_Oinverse__class_Oinverse_type,type,
c_Rings_Oinverse__class_Oinverse: $i > $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_fequal_type,type,
c_fequal: $i > $i > $i ).
thf(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $i > $o ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(c_Polynomial_Omonom_type,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(class_Rings_Oordered__comm__semiring_type,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_type,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(class_Rings_Odvd_type,type,
class_Rings_Odvd: $i > $o ).
thf(class_Rings_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Divides_Oring__div_type,type,
class_Divides_Oring__div: $i > $o ).
thf(class_Fields_Ofield__inverse__zero_type,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_Groups_Ouminus_type,type,
class_Groups_Ouminus: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Fields_Olinordered__field__inverse__zero_type,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(c_Groups_Osgn__class_Osgn_type,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(c_Polynomial_Opoly__gcd_type,type,
c_Polynomial_Opoly__gcd: $i > $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: $i > $i > $i > $i ).
thf(class_Groups_Osgn__if_type,type,
class_Groups_Osgn__if: $i > $o ).
thf(class_Rings_Olinordered__semiring_type,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_type,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_Polynomial_Ocoeff_type,type,
c_Polynomial_Ocoeff: $i > $i > $i ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(class_Rings_Oordered__semiring_type,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_Rings_Oordered__ring_type,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_type,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Groups_Ominus_type,type,
class_Groups_Ominus: $i > $o ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Olinordered__semiring__1__strict_type,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
thf(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Groups_Omonoid__add_type,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Groups_Ogroup__add_type,type,
class_Groups_Ogroup__add: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_Rings_Osemiring_type,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(c_Nat_Onat_Onat__case_type,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Polynomial_OAbs__poly_type,type,
c_Polynomial_OAbs__poly: $i > $i > $i ).
thf(class_RealVector_Oreal__normed__div__algebra_type,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(c_Polynomial_Opoly__rec_type,type,
c_Polynomial_Opoly__rec: $i > $i > $i > $i > $i > $i ).
thf(c_If_type,type,
c_If: $i > $i > $i > $i > $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Ocomm__ring_type,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(c_Polynomial_Osynthetic__div_type,type,
c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_type,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Groups_Ocancel__comm__monoid__add_type,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Rings_Osemiring__0_type,type,
class_Rings_Osemiring__0: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: $i > $i > $i > $i ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_type,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_type,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(c_Nat_Onat_Onat__size_type,type,
c_Nat_Onat_Onat__size: $i > $i ).
thf(c_Polynomial_Opcompose_type,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(class_RealVector_Oreal__field_type,type,
class_RealVector_Oreal__field: $i > $o ).
thf(class_Rings_Ocomm__semiring_type,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(c_Groups_Osemigroup_type,type,
c_Groups_Osemigroup: $i > $i > $o ).
thf(c_Groups_Ocomm__monoid_type,type,
c_Groups_Ocomm__monoid: $i > $i > $i > $o ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
thf(1501,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(983,axiom,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
thf(4447,plain,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono) ).
thf(3883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(869,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).
thf(4094,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
thf(2778,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ B )
= ( c_Power_Opower__class_Opower @ C @ B @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(3661,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ B )
= ( c_Power_Opower__class_Opower @ C @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(748,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Omonom @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__0) ).
thf(3666,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Omonom @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(1982,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
thf(2559,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).
thf(2544,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1818,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
thf(1956,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(616,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
thf(3172,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(345,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(2199,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(581,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(3021,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
<=> ( ( c_Polynomial_Opos__poly @ C @ A )
| ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
thf(1036,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
=> ( ( c_Polynomial_Opos__poly @ C @ A )
| ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) )
& ( ( ( c_Polynomial_Opos__poly @ C @ A )
| ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) )
=> ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
thf(3873,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
thf(4188,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(2744,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
<=> ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
thf(1369,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) )
& ( ( c_Rings_Odvd__class_Odvd @ C @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(986,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(4450,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(2341,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
thf(2412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).
thf(1237,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(3698,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(837,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(3979,plain,
class_Rings_Osemiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__case @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(2463,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__case @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(1899,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( c_Polynomial_Ocoeff @ C @ B )
= ( c_Polynomial_Ocoeff @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__inject) ).
thf(3863,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( ( c_Polynomial_Ocoeff @ C @ B )
= ( c_Polynomial_Ocoeff @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Polynomial_Ocoeff @ C @ B )
= ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse) ).
thf(2595,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B = A )
<=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
thf(1158,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) )
& ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(595,axiom,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(3072,plain,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(555,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(2940,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono) ).
thf(2381,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).
thf(2395,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(172,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
thf(1591,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2837,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).
thf(1305,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(998,axiom,
class_Rings_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
thf(4487,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
| ( c_Polynomial_Opos__poly @ C @ A )
| ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ),
inference(cnf,[status(esa)],[1036]) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
| ( c_Polynomial_Opos__poly @ C @ A ) ),
inference(lifteq,[status(thm)],[1037]) ).
thf(383,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(2363,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( c_Groups_Otimes__class_Otimes @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(2077,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( c_Groups_Otimes__class_Otimes @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Omonom @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Polynomial_OpCons @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__0) ).
thf(3534,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Omonom @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Polynomial_OpCons @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(3317,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1004,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(4500,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(1013,axiom,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
thf(4515,plain,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(815,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__pCons__Suc) ).
thf(3905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(146,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(1522,plain,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(1808,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(674,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(3417,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).
thf(3509,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(645,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(3285,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
= ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
thf(2527,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
= ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(960,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ C @ B ) ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
thf(4391,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ C @ B ) ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(2953,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Osmult @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) @ A ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__code) ).
thf(1401,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Osmult @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) @ A ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).
thf(1422,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(2947,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
thf(1569,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(477,axiom,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
thf(2671,plain,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ A @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ B @ A ) ) @ ( c_Polynomial_OpCons @ D @ C @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
thf(3910,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ A @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ B @ A ) ) @ ( c_Polynomial_OpCons @ D @ C @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(1793,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(530,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(2854,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Odiff) ).
thf(1692,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Oring__char__0 @ C )
& ( class_Rings_Oidom @ C ) )
=> ( ( ( c_Polynomial_Opoly @ C @ B )
= ( c_Polynomial_Opoly @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
thf(4408,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Oring__char__0 @ C )
& ( class_Rings_Oidom @ C ) )
=> ( ( ( ( c_Polynomial_Opoly @ C @ B )
= ( c_Polynomial_Opoly @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Polynomial_Opoly @ C @ B )
= ( c_Polynomial_Opoly @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(134,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
thf(1486,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Rings_Ocomm__ring @ D )
& ( class_Rings_Odvd @ D ) )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ! [E: $i,F: $i] :
( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
<=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( c_Groups_Otimes__class_Otimes @ D @ F @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
thf(4105,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Rings_Ocomm__ring @ D )
& ( class_Rings_Odvd @ D ) )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ! [E: $i,F: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( c_Groups_Otimes__class_Otimes @ D @ F @ B ) ) @ A ) ) )
& ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( c_Groups_Otimes__class_Otimes @ D @ F @ B ) ) @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A )
<=> ( B
= ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
thf(1671,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A )
=> ( B
= ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
& ( ( B
= ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(1655,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__mult) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opcompose @ C @ B @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pcompose__le) ).
thf(4279,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opcompose @ C @ B @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Groups_Osemigroup @ E @ D )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ ( hAPP @ D @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ D @ C ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semigroup_Oassoc) ).
thf(4440,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Groups_Osemigroup @ E @ D )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ ( hAPP @ D @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ D @ C ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(3693,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(1919,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(978,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(4435,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
thf(1458,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(1497,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1025,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(4543,plain,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
thf(3049,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
thf(3745,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(972,axiom,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
thf(4418,plain,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
thf(2607,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
thf(2686,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(3004,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ouminus @ D )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ D @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).
thf(2035,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ouminus @ D )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ D @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(659,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__0) ).
thf(3367,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(826,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(3942,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(846,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ D ) ) @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__lemma) ).
thf(4011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ D ) ) @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(741,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(3649,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(608,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(3135,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Oring__char__0 @ B )
& ( class_Rings_Oidom @ B ) )
=> ( ( ( c_Polynomial_Opoly @ B @ A )
= ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__zero) ).
thf(4097,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Oring__char__0 @ B )
& ( class_Rings_Oidom @ B ) )
=> ( ( ( ( c_Polynomial_Opoly @ B @ A )
= ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Polynomial_Opoly @ B @ A )
= ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(3365,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(494,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
thf(2740,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
thf(4110,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ ( c_Polynomial_Osmult @ D @ C @ A ) )
<=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
thf(4220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ ( c_Polynomial_Osmult @ D @ C @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) )
& ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(408,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( c_Polynomial_Odegree @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__0) ).
thf(2448,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( c_Polynomial_Odegree @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1819,plain,
( ! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(miniscope,[status(thm)],[1818]) ).
thf(1820,plain,
! [B: $i,A: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(cnf,[status(esa)],[1819]) ).
thf(1823,plain,
! [B: $i,A: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(lifteq,[status(thm)],[1820]) ).
thf(1824,plain,
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(simp,[status(thm)],[1823]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_p ) )
& ! [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_p ) )
& ! [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1030,plain,
~ ? [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_p ) )
& ! [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1031,plain,
! [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
!= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_p ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ ( sk1 @ A ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[1030]) ).
thf(1032,plain,
! [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
!= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_p ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ ( sk1 @ A ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[1031]) ).
thf(4556,plain,
! [A: $i] :
( ( tc_Complex_Ocomplex != tc_Complex_Ocomplex )
| ( A != v_p )
| ( ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A )
!= ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[1032]) ).
thf(4558,plain,
( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) ),
inference(simp,[status(thm)],[4556]) ).
thf(11793,plain,
( ( ( sk1 @ v_p )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
!= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) ),
inference(paramod_ordered,[status(thm)],[1824,4558]) ).
thf(11859,plain,
( ( ( sk1 @ v_p )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( tc_Nat_Onat != tc_Complex_Ocomplex )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= v_a )
| ( ( sk1 @ v_p )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(simp,[status(thm)],[11793]) ).
thf(11917,plain,
( ( ( sk1 @ v_p )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( tc_Nat_Onat != tc_Complex_Ocomplex )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= v_a ) ),
inference(simp,[status(thm)],[11859]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__dvd2) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
thf(4058,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__diff) ).
thf(3370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield__inverse__zero @ B )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
thf(1196,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield__inverse__zero @ B )
=> ( ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(3236,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(706,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(3545,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
| ( c_Polynomial_Opos__poly @ B @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__total) ).
thf(1044,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
| ( c_Polynomial_Opos__poly @ B @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
| ( c_Polynomial_Opos__poly @ B @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[1044]) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
| ~ ( class_Rings_Olinordered__idom @ B )
| ( c_Polynomial_Opos__poly @ B @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ),
inference(lifteq,[status(thm)],[1045]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(1601,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(901,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
thf(4198,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(4030,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).
thf(3809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(4467,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
thf(2869,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1009,axiom,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
thf(4511,plain,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).
thf(2432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(3994,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( ( c_Polynomial_Omonom @ D @ C @ B )
= ( c_Polynomial_Omonom @ D @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
thf(1243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( ( ( c_Polynomial_Omonom @ D @ C @ B )
= ( c_Polynomial_Omonom @ D @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( c_Polynomial_Omonom @ D @ C @ B )
= ( c_Polynomial_Omonom @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(27,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
thf(1127,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
thf(3915,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(230,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(1782,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1002,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
thf(4496,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(166,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(1576,plain,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(4079,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(45,axiom,
! [A: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
thf(1189,plain,
! [A: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1190,plain,
( ! [A: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ! [A: $i] :
( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(miniscope,[status(thm)],[1189]) ).
thf(1191,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(cnf,[status(esa)],[1190]) ).
thf(1193,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(lifteq,[status(thm)],[1191]) ).
thf(1194,plain,
c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ),
inference(simp,[status(thm)],[1193]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
<=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
thf(1060,plain,
! [A: $i,B: $i] :
( ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ( B != A ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1061,plain,
( ! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) )
& ! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ( B != A ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[1060]) ).
thf(1063,plain,
! [B: $i,A: $i] :
( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
| ( B = A )
| ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ),
inference(cnf,[status(esa)],[1061]) ).
thf(1068,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
| ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ),
inference(lifteq,[status(thm)],[1063]) ).
thf(1069,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
| ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ),
inference(simp,[status(thm)],[1068]) ).
thf(8986,plain,
! [B: $i,A: $i] :
( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
| ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ v_p ) )
| ( B != v_p ) ),
inference(paramod_ordered,[status(thm)],[1069,4558]) ).
thf(8987,plain,
! [A: $i] :
( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_p @ A )
| ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ v_p )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[8986:[bind(A,$thf( A )),bind(B,$thf( v_p ))]]) ).
thf(10407,plain,
! [A: $i] :
( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ v_p )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ v_p ) )
| ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
!= ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1194,8987]) ).
thf(10475,plain,
! [A: $i] :
( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ v_p )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ v_p ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= v_p )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= A ) ),
inference(simp,[status(thm)],[10407]) ).
thf(10503,plain,
( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_p )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
!= ( sk1 @ v_p ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= v_p ) ),
inference(simp,[status(thm)],[10475]) ).
thf(11422,plain,
( ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
!= ( sk1 @ v_p ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= v_p )
| ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
!= ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_p ) ) ),
inference(paramod_ordered,[status(thm)],[1194,10503]) ).
thf(11519,plain,
( ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
!= ( sk1 @ v_p ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= v_p )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= v_p ) ),
inference(simp,[status(thm)],[11422]) ).
thf(11568,plain,
( ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
!= ( sk1 @ v_p ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= v_p ) ),
inference(simp,[status(thm)],[11519]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
<=> ( ( B = A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).
thf(1049,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
=> ( ( B = A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) )
& ( ( ( B = A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
| ( B = A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ),
inference(cnf,[status(esa)],[1049]) ).
thf(1053,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ),
inference(lifteq,[status(thm)],[1050]) ).
thf(6408,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ v_p ) )
| ( B != v_p ) ),
inference(paramod_ordered,[status(thm)],[1053,4558]) ).
thf(6409,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ B ) @ v_p @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ v_p ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[6408:[bind(A,$thf( A )),bind(B,$thf( v_p ))]]) ).
thf(6904,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ B ) @ v_p @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ v_p ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[6409]) ).
thf(276,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(1935,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__mod__less) ).
thf(3947,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).
thf(1650,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
thf(3730,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
thf(1645,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(934,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(4322,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(2819,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(5136,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ( c_Polynomial_Opos__poly @ B @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) )
!= ( sk1 @ v_p ) )
| ( A
!= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) ),
inference(paramod_ordered,[status(thm)],[1046,4558]) ).
thf(5137,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[5136:[bind(A,$thf( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) )),bind(B,$thf( B ))]]) ).
thf(5269,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[5137]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
thf(2136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(1703,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).
thf(1623,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
thf(3597,plain,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(470,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(2654,plain,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(3976,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A )
=> ( ! [E: $i] :
( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ E @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ E @ A )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ E @ C ) ) )
=> ( ( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ~ ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) )
= ( c_Groups_Oone__class_Oone @ D ) ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ D @ B @ A )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__unique) ).
thf(1430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A )
=> ( ! [E: $i] :
( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ E @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ E @ A )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ E @ C ) ) )
=> ( ( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ~ ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) )
= ( c_Groups_Oone__class_Oone @ D ) ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ D @ B @ A )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
thf(2814,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(885,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(4151,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__1__left) ).
thf(3046,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(969,axiom,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
thf(4415,plain,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__zero__or__degree__less) ).
thf(1907,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(3148,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(3485,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(3776,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(167,axiom,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(1577,plain,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
thf(2562,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(2466,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(634,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__one) ).
thf(3248,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ( B != A )
| ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ),
inference(cnf,[status(esa)],[1049]) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ( B != A )
| ~ ( class_Rings_Olinordered__idom @ C )
| ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ),
inference(lifteq,[status(thm)],[1052]) ).
thf(1055,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ B ) @ A @ A ) ),
inference(simp,[status(thm)],[1054]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Polynomial_Omonom @ D @ B @ A ) )
= ( c_Polynomial_Omonom @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__monom) ).
thf(4238,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Polynomial_Omonom @ D @ B @ A ) )
= ( c_Polynomial_Omonom @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(3204,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(980,axiom,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
thf(4439,plain,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
thf(3221,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(3029,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(945,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
thf(4348,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(2698,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(224,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ominus @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
thf(1760,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ominus @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(1660,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(500,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
thf(2755,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(692,axiom,
class_Rings_Odvd @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
thf(3495,plain,
class_Rings_Odvd @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
thf(1264,plain,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(937,axiom,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(4334,plain,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( B = A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
thf(1313,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( B = A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(4349,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(4428,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Polynomial_Opos__poly @ C @ B )
=> ( ( c_Polynomial_Opos__poly @ C @ A )
=> ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
thf(1058,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Polynomial_Opos__poly @ C @ B )
=> ( ( c_Polynomial_Opos__poly @ C @ A )
=> ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1059,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ B )
| ~ ( c_Polynomial_Opos__poly @ C @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ),
inference(cnf,[status(esa)],[1058]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(3043,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A )
<=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
thf(2571,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
= B ) )
& ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
= B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(762,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(3713,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(599,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(3099,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(4353,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(3638,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__add) ).
thf(1319,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
= ( c_Groups_Oone__class_Oone @ C ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
thf(2767,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
= ( c_Groups_Oone__class_Oone @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
thf(1609,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(218,axiom,
class_Groups_Ominus @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(1741,plain,
class_Groups_Ominus @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1029,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__1) ).
thf(4551,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(4141,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(2989,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).
thf(1100,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(1847,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).
thf(1545,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).
thf(2420,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
thf(1922,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
thf(2691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(877,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(4119,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(698,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(3517,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(800,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(3840,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( D = C )
=> ( B = A ) )
& ( ( B = A )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(3385,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(6410,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ A @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) )
| ( B != v_a ) ),
inference(paramod_ordered,[status(thm)],[1053,4558]) ).
thf(6411,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ B ) @ v_a @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ v_a ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ A @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[6410:[bind(A,$thf( A )),bind(B,$thf( v_a ))]]) ).
thf(6905,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ B ) @ v_a @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ v_a ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ A @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[6411]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(1147,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(2373,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(821,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(3919,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(93,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
thf(1347,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__greatest) ).
thf(1572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E @ C @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2635,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E @ C @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(3470,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(956,axiom,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
thf(4383,plain,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(1815,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(4460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(619,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( c_Polynomial_OpCons @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
thf(3180,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( ( c_Polynomial_OpCons @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( c_Polynomial_OpCons @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(993,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(4471,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(1007,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(4507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__inverse) ).
thf(3602,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1875,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1012,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(4514,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A )
<=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(2388,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) )
& ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Osmult @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult) ).
thf(3268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Osmult @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(637,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(3258,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(4554,plain,
! [A: $i] :
( ( tc_Complex_Ocomplex != tc_Complex_Ocomplex )
| ( A != v_p )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ ( sk1 @ A ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) ) ) ) ),
inference(simp,[status(thm)],[1032]) ).
thf(4557,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[4554]) ).
thf(4653,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
| ( c_Polynomial_Opos__poly @ C @ A )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) )
| ( A
!= ( sk1 @ v_p ) ) ),
inference(paramod_ordered,[status(thm)],[1041,4557]) ).
thf(4654,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( sk1 @ v_p ) ) )
| ( c_Polynomial_Opos__poly @ B @ ( sk1 @ v_p ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) ) ),
inference(pattern_uni,[status(thm)],[4653:[bind(A,$thf( sk1 @ v_p )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4756,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( sk1 @ v_p ) ) )
| ( c_Polynomial_Opos__poly @ B @ ( sk1 @ v_p ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) ) ),
inference(simp,[status(thm)],[4654]) ).
thf(788,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(3788,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(5072,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ( c_Polynomial_Opos__poly @ B @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) )
| ( A
!= ( sk1 @ v_p ) ) ),
inference(paramod_ordered,[status(thm)],[1046,4557]) ).
thf(5073,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( sk1 @ v_p ) )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( sk1 @ v_p ) ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) ) ),
inference(pattern_uni,[status(thm)],[5072:[bind(A,$thf( sk1 @ v_p )),bind(B,$thf( B ))]]) ).
thf(5345,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( sk1 @ v_p ) )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( sk1 @ v_p ) ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) ) ),
inference(simp,[status(thm)],[5073]) ).
thf(5745,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( sk1 @ v_p ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) )
| ( ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( sk1 @ v_p ) ) )
!= ( c_Polynomial_Opos__poly @ A @ ( sk1 @ v_p ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5345]) ).
thf(5768,plain,
! [A: $i] :
( ( c_Polynomial_Opos__poly @ A @ ( sk1 @ v_p ) )
| ~ ( class_Rings_Olinordered__idom @ A )
| ( ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p )
!= ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
!= ( sk1 @ v_p ) )
| ( A != A )
| ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[5745]) ).
thf(5792,plain,
! [A: $i] :
( ( c_Polynomial_Opos__poly @ A @ ( sk1 @ v_p ) )
| ~ ( class_Rings_Olinordered__idom @ A )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
!= ( sk1 @ v_p ) )
| ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[5768]) ).
thf(559,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(2950,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(280,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__0__0) ).
thf(1946,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(596,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
thf(3075,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ominus) ).
thf(2259,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(409,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).
thf(2451,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(3973,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
thf(1151,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(434,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(2540,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).
thf(1283,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(296,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
thf(2017,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
thf(1302,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(2794,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(4329,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(4258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
thf(1373,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(766,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
thf(3724,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[1036]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ ( c_Polynomial_Odegree @ C @ B ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__mult__degree__sum) ).
thf(1632,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ ( c_Polynomial_Odegree @ C @ B ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(3163,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(2650,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__inverse) ).
thf(1334,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(3473,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mod__geq) ).
thf(3983,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(539,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(2880,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
thf(1682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(680,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
<=> ( ( D
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ E ) @ B @ C ) @ A ) )
& ( ( C
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ E @ A ) @ ( c_Polynomial_Odegree @ E @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).
thf(3438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
=> ( ( D
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ E ) @ B @ C ) @ A ) )
& ( ( C
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ E @ A ) @ ( c_Polynomial_Odegree @ E @ C ) ) ) ) ) )
& ( ( ( D
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ E ) @ B @ C ) @ A ) )
& ( ( C
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ E @ A ) @ ( c_Polynomial_Odegree @ E @ C ) ) ) ) )
=> ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(860,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(4050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B )
= A ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B )
= A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(2122,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
thf(3525,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(254,axiom,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
thf(1864,plain,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(106,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(1383,plain,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
thf(2254,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
thf(3923,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq) ).
thf(3300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1051,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
| ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ),
inference(cnf,[status(esa)],[1049]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(3771,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(665,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(3389,plain,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(840,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(3986,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
thf(1169,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(3537,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(2190,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
thf(3157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Oorder @ C @ A @ B ) @ ( c_Polynomial_Odegree @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__degree) ).
thf(2286,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Oorder @ C @ A @ B ) @ ( c_Polynomial_Odegree @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( ( c_Polynomial_Osynthetic__div @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
<=> ( ( c_Polynomial_Odegree @ C @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
thf(2103,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( ( ( c_Polynomial_Osynthetic__div @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( c_Polynomial_Odegree @ C @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Polynomial_Osynthetic__div @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Nat_OSuc @ B )
!= A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1943,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Nat_OSuc @ B )
!= A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(905,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(4211,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leading__coeff__neq__0) ).
thf(3492,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(4033,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
thf(2618,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ ( c_Polynomial_Osmult @ D @ C @ A ) )
= ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__smult__right) ).
thf(2281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ ( c_Polynomial_Osmult @ D @ C @ A ) )
= ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(2861,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(49,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
thf(1215,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(3685,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(1886,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ E ) @ D @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__poly__eq) ).
thf(1072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ E ) @ D @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
!= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).
thf(2530,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
!= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(2523,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
thf(1119,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
thf(4087,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(2979,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(657,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(3361,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1022,axiom,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
thf(4536,plain,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
thf(3243,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(2809,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(564,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
thf(2965,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ocomm__monoid @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid_Ocomm__neutral) ).
thf(4519,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ocomm__monoid @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(954,axiom,
class_Fields_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
thf(4379,plain,
class_Fields_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(206,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1697,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(205,axiom,
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(1695,plain,
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1696,plain,
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(lifteq,[status(thm)],[1695]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(2586,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(2982,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
thf(2884,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(3435,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(3582,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(996,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(4480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
thf(4531,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
thf(2047,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).
thf(1470,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(2641,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1073,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Fields_Ofield @ E )
| ~ ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ E ) @ D @ C )
= A ) ),
inference(cnf,[status(esa)],[1072]) ).
thf(1074,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ E ) @ D @ C )
= A )
| ~ ( class_Fields_Ofield @ E )
| ~ ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A ) ),
inference(lifteq,[status(thm)],[1073]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osmult @ C @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osmult @ C @ B @ A ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__smult__eq) ).
thf(3899,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osmult @ C @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osmult @ C @ B @ A ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(3567,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(203,axiom,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1688,plain,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1689,plain,
~ ? [A: $i] :
( A
= ( c_Nat_OSuc @ A ) ),
inference(miniscope,[status(thm)],[1688]) ).
thf(1690,plain,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
inference(cnf,[status(esa)],[1689]) ).
thf(1691,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
inference(lifteq,[status(thm)],[1690]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__0) ).
thf(3531,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(736,axiom,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(3635,plain,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).
thf(4076,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(953,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(4370,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(493,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(2737,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(3054,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).
thf(1736,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(421,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(2496,plain,
class_Rings_Omult__zero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
& ! [D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(4312,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
& ! [D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(509,axiom,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(2790,plain,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
= ( c_Power_Opower__class_Opower @ D @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
= ( c_Power_Opower__class_Opower @ D @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( B
= ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1768,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( B
= ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(3550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(4172,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(2773,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(6,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ~ ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
thf(1047,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ~ ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(1730,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Polynomial_Opos__poly @ C @ B )
=> ( ( c_Polynomial_Opos__poly @ C @ A )
=> ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__add) ).
thf(1056,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Polynomial_Opos__poly @ C @ B )
=> ( ( c_Polynomial_Opos__poly @ C @ A )
=> ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ B )
| ~ ( c_Polynomial_Opos__poly @ C @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ),
inference(cnf,[status(esa)],[1056]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
thf(1274,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__neg) ).
thf(1387,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(638,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(3261,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(990,axiom,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
thf(4466,plain,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(4016,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(356,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(2249,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(2541,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
inference(cnf,[status(esa)],[2540]) ).
thf(95,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
thf(1355,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
thf(2133,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(50,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
thf(1217,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_OAbs__poly @ B @ ( c_Polynomial_Ocoeff @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__inverse) ).
thf(2937,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_OAbs__poly @ B @ ( c_Polynomial_Ocoeff @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(985,axiom,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
thf(4449,plain,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(301,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(2032,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(2890,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__antisym) ).
thf(1519,plain,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(962,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
thf(4397,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(3742,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(2969,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(4128,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(3069,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(4160,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(747,axiom,
( ( c_Nat_Onat_Onat__size @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
thf(3664,plain,
( ( c_Nat_Onat_Onat__size @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(4323,plain,
( ! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ! [A: $i] :
( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(miniscope,[status(thm)],[4322]) ).
thf(4324,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(cnf,[status(esa)],[4323]) ).
thf(4326,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(lifteq,[status(thm)],[4324]) ).
thf(4327,plain,
c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(simp,[status(thm)],[4326]) ).
thf(489,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(2724,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(2725,plain,
( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(lifteq,[status(thm)],[2724]) ).
thf(11102,plain,
c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ),
inference(rewrite,[status(thm)],[4327,2725]) ).
thf(886,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(4152,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(4153,plain,
~ ? [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
inference(miniscope,[status(thm)],[4152]) ).
thf(4154,plain,
! [B: $i,A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
inference(cnf,[status(esa)],[4153]) ).
thf(11126,plain,
! [B: $i,A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
!= ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(paramod_ordered,[status(thm)],[11102,4154]) ).
thf(11172,plain,
! [B: $i,A: $i] :
( ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(simp,[status(thm)],[11126]) ).
thf(11191,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(simp,[status(thm)],[11172]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(3207,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(753,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(3682,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(4021,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(3778,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(295,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
thf(2015,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(1883,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__div) ).
thf(1560,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(881,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(4140,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Fields_Ofield @ F )
=> ( ( c_Polynomial_Opdivmod__rel @ F @ E @ D @ C @ B )
=> ( c_Polynomial_Opdivmod__rel @ F @ ( c_Polynomial_Osmult @ F @ A @ E ) @ D @ ( c_Polynomial_Osmult @ F @ A @ C ) @ ( c_Polynomial_Osmult @ F @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__left) ).
thf(1365,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Fields_Ofield @ F )
=> ( ( c_Polynomial_Opdivmod__rel @ F @ E @ D @ C @ B )
=> ( c_Polynomial_Opdivmod__rel @ F @ ( c_Polynomial_Osmult @ F @ A @ E ) @ D @ ( c_Polynomial_Osmult @ F @ A @ C ) @ ( c_Polynomial_Osmult @ F @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(5448,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) )
| ( ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) )
!= ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5269]) ).
thf(5451,plain,
! [A: $i] :
( ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ~ ( class_Rings_Olinordered__idom @ A )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) )
| ( A != A )
| ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) ),
inference(simp,[status(thm)],[5448]) ).
thf(5465,plain,
! [A: $i] :
( ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ~ ( class_Rings_Olinordered__idom @ A )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) )
| ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) ),
inference(simp,[status(thm)],[5451]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(3578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(4696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
| ( c_Polynomial_Opos__poly @ C @ A )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) )
!= ( sk1 @ v_p ) )
| ( A
!= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) ),
inference(paramod_ordered,[status(thm)],[1041,4558]) ).
thf(4697,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) )
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[4696:[bind(A,$thf( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4746,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[4697]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Osgn__if @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__if) ).
thf(1836,plain,
! [A: $i,B: $i] :
( ( class_Groups_Osgn__if @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
<=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(1076,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1077,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Groups_Oordered__ab__group__add @ E )
| ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
!= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
| ~ ( c_Orderings_Oord__class_Oless @ E @ B @ A )
| ( c_Orderings_Oord__class_Oless @ E @ D @ C ) ),
inference(cnf,[status(esa)],[1076]) ).
thf(1079,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
!= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
| ~ ( class_Groups_Oordered__ab__group__add @ E )
| ~ ( c_Orderings_Oord__class_Oless @ E @ B @ A )
| ( c_Orderings_Oord__class_Oless @ E @ D @ C ) ),
inference(lifteq,[status(thm)],[1077]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
thf(1407,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) @ B )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
thf(3763,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) @ B )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(768,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Polynomial_Opcompose @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__0) ).
thf(3727,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Polynomial_Opcompose @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__poly__less) ).
thf(1291,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
<=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
thf(3166,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__eq__0) ).
thf(3958,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ozero @ F )
=> ( ( c_Polynomial_Opoly__rec @ E @ F @ D @ C @ ( c_Polynomial_OpCons @ F @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ C @ B ) @ A ) @ ( c_If @ E @ ( c_fequal @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ F ) ) ) @ D @ ( c_Polynomial_Opoly__rec @ E @ F @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
thf(1938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ozero @ F )
=> ( ( c_Polynomial_Opoly__rec @ E @ F @ D @ C @ ( c_Polynomial_OpCons @ F @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ C @ B ) @ A ) @ ( c_If @ E @ ( c_fequal @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ F ) ) ) @ D @ ( c_Polynomial_Opoly__rec @ E @ F @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(2758,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
thf(3980,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(670,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) @ B )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
thf(3403,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) @ B )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(445,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Polynomial_Osmult @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__left) ).
thf(2565,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Polynomial_Osmult @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(2663,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Polynomial_Opoly__gcd @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Ocommute) ).
thf(1555,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Polynomial_Opoly__gcd @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(4155,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(3314,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(3499,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(3750,plain,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(3556,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
thf(2872,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(4385,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq) ).
thf(1888,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(764,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(3718,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ B )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
thf(3894,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ B )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
thf(2068,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(971,axiom,
class_Rings_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
thf(4417,plain,
class_Rings_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ ( c_Polynomial_Oorder @ C @ A @ B ) ) @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order) ).
thf(3926,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ ( c_Polynomial_Oorder @ C @ A @ B ) ) @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3931,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(217,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(1739,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1740,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__semidom @ A )
| ~ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(cnf,[status(esa)],[1739]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).
thf(1910,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
thf(4027,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__def) ).
thf(4316,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
thf(1360,plain,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
| ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(3467,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).
thf(1762,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
thf(1328,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).
thf(3632,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(1749,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1750,plain,
( ! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(miniscope,[status(thm)],[1749]) ).
thf(1751,plain,
! [B: $i,A: $i] :
( ( B
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( A
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(cnf,[status(esa)],[1750]) ).
thf(1754,plain,
! [B: $i,A: $i] :
( ( B
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( A
!= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(lifteq,[status(thm)],[1751]) ).
thf(1755,plain,
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(simp,[status(thm)],[1754]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(2638,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(2268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).
thf(1089,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(785,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(3780,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(3781,plain,
~ ? [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
inference(miniscope,[status(thm)],[3780]) ).
thf(3782,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
inference(cnf,[status(esa)],[3781]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( c_fequal @ B @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1234,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( c_fequal @ B @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(798,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).
thf(3831,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(2840,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odvd @ D )
=> ( ( C
= ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvdI) ).
thf(1143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odvd @ D )
=> ( ( C
= ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) )
<=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
& ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__poly__gcd__iff) ).
thf(1270,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
& ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) )
& ( ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
& ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Osmult @ D @ B @ A ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
thf(1851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Osmult @ D @ B @ A ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(5138,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ( c_Polynomial_Opos__poly @ B @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
!= ( sk1 @ v_p ) )
| ( A
!= ( sk1 @ v_p ) ) ),
inference(paramod_ordered,[status(thm)],[1046,4558]) ).
thf(5139,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( sk1 @ v_p ) )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( sk1 @ v_p ) ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[5138:[bind(A,$thf( sk1 @ v_p )),bind(B,$thf( B ))]]) ).
thf(5270,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( sk1 @ v_p ) )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( sk1 @ v_p ) ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[5139]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).
thf(2801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
thf(1534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1010,axiom,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
thf(4512,plain,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).
thf(4248,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(25,axiom,
! [A: $i] :
( ( class_Rings_Odivision__ring @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__1) ).
thf(1121,plain,
! [A: $i] :
( ( class_Rings_Odivision__ring @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(997,axiom,
class_Groups_Ouminus @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
thf(4486,plain,
class_Groups_Ouminus @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(2709,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(1970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(628,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).
thf(3218,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(859,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(4048,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1026,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
thf(4544,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( c_fequal @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1096,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( c_fequal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(2509,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(3102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).
thf(1540,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(3518,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
thf(1878,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(490,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
thf(2726,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).
thf(1138,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(1719,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(532,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(2858,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__minus) ).
thf(2537,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(580,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(3018,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
thf(1397,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(3326,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(2791,plain,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ),
inference(cnf,[status(esa)],[2790]) ).
thf(12179,plain,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ),
inference(rewrite,[status(thm)],[2791,2725]) ).
thf(521,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(2830,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(12,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(1075,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__0 @ E )
=> ( ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ D @ ( c_Polynomial_Osmult @ E @ C @ B ) )
= ( c_Polynomial_OpCons @ E @ A @ B ) )
=> ( ( A
= ( hAPP @ ( c_Polynomial_Opoly @ E @ D ) @ C ) )
& ( B
= ( c_Polynomial_Osynthetic__div @ E @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
thf(4545,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__0 @ E )
=> ( ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ D @ ( c_Polynomial_Osmult @ E @ C @ B ) )
= ( c_Polynomial_OpCons @ E @ A @ B ) )
=> ( ( A
= ( hAPP @ ( c_Polynomial_Opoly @ E @ D ) @ C ) )
& ( B
= ( c_Polynomial_Osynthetic__div @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
thf(1612,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(647,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(3294,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(2460,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
thf(1493,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(650,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ ( c_Polynomial_Osynthetic__div @ C @ A @ B ) ) @ ( c_Polynomial_OpCons @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
thf(3311,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ ( c_Polynomial_Osynthetic__div @ C @ A @ B ) ) @ ( c_Polynomial_OpCons @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2877,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__add) ).
thf(4425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_Opcompose @ D @ C @ B ) ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pcompose) ).
thf(4421,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_Opcompose @ D @ C @ B ) ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(1424,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(2312,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(2053,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Omonom @ C @ B @ A ) )
= ( c_Polynomial_Omonom @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__monom) ).
thf(2196,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Omonom @ C @ B @ A ) )
= ( c_Polynomial_Omonom @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( c_Polynomial_Opdivmod__rel @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0) ).
thf(4191,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( c_Polynomial_Opdivmod__rel @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1011,axiom,
class_Groups_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
thf(4513,plain,
class_Groups_Ozero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(1698,plain,
~ ? [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(miniscope,[status(thm)],[1697]) ).
thf(1699,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(cnf,[status(esa)],[1698]) ).
thf(1700,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(lifteq,[status(thm)],[1699]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
<=> ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
= ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
thf(2613,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
= ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) )
& ( ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
= ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(2172,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(319,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(2108,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
thf(2038,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(439,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
thf(2551,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(3671,plain,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
thf(3643,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osynthetic__div @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
= ( c_Polynomial_OpCons @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) @ ( c_Polynomial_Osynthetic__div @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
thf(4444,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osynthetic__div @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
= ( c_Polynomial_OpCons @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) @ ( c_Polynomial_Osynthetic__div @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__degree__le) ).
thf(3573,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(2225,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(2226,plain,
( ! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(miniscope,[status(thm)],[2225]) ).
thf(2229,plain,
! [B: $i,A: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(cnf,[status(esa)],[2226]) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
!= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(lifteq,[status(thm)],[2229]) ).
thf(2238,plain,
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(simp,[status(thm)],[2237]) ).
thf(12314,plain,
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(rewrite,[status(thm)],[2238,2725]) ).
thf(506,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
thf(2781,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(1019,axiom,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
thf(4530,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).
thf(1419,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
thf(1451,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1668,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(1932,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).
thf(3819,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Polynomial_OpCons @ D @ B @ A ) )
= ( c_Polynomial_OpCons @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__pCons) ).
thf(1799,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Polynomial_OpCons @ D @ B @ A ) )
= ( c_Polynomial_OpCons @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).
thf(3628,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(970,axiom,
class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
thf(4416,plain,
class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(3703,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(565,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(2968,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(85,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
thf(1324,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
thf(1114,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__zero__iff) ).
thf(3611,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(3656,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
thf(2125,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(743,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
thf(3654,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(1588,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
thf(1478,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(60,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(1249,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(427,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ouminus @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
thf(2519,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ouminus @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(957,axiom,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
thf(4384,plain,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(124,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
thf(1456,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(105,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(1382,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( ( c_Polynomial_Osmult @ D @ C @ B )
= ( c_Polynomial_OpCons @ D @ A @ B ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
thf(2487,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( ( c_Polynomial_Osmult @ D @ C @ B )
= ( c_Polynomial_OpCons @ D @ A @ B ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ! [D: $i] :
( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ C @ D @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ D @ B ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).
thf(2845,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ! [D: $i] :
( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ C @ D @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ D @ B ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(454,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(2598,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(245,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(1831,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__mod) ).
thf(1231,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(2153,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A )
<=> ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
thf(2900,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A )
=> ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) )
& ( ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A )
= ( c_Polynomial_Osmult @ D @ C @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__smult__left) ).
thf(2851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A )
= ( c_Polynomial_Osmult @ D @ C @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ G ) ) )
=> ( ( B
= ( c_Rings_Oinverse__class_Odivide @ G @ ( hAPP @ ( c_Polynomial_Ocoeff @ G @ ( c_Polynomial_OpCons @ G @ A @ C ) ) @ ( c_Polynomial_Odegree @ G @ E ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ G @ E ) @ ( c_Polynomial_Odegree @ G @ E ) ) ) )
=> ( c_Polynomial_Opdivmod__rel @ G @ ( c_Polynomial_OpCons @ G @ A @ F ) @ E @ ( c_Polynomial_OpCons @ G @ B @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ G ) @ ( c_Polynomial_OpCons @ G @ A @ C ) @ ( c_Polynomial_Osmult @ G @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__pCons) ).
thf(2243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ G ) ) )
=> ( ( B
= ( c_Rings_Oinverse__class_Odivide @ G @ ( hAPP @ ( c_Polynomial_Ocoeff @ G @ ( c_Polynomial_OpCons @ G @ A @ C ) ) @ ( c_Polynomial_Odegree @ G @ E ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ G @ E ) @ ( c_Polynomial_Odegree @ G @ E ) ) ) )
=> ( c_Polynomial_Opdivmod__rel @ G @ ( c_Polynomial_OpCons @ G @ A @ F ) @ E @ ( c_Polynomial_OpCons @ G @ B @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ G ) @ ( c_Polynomial_OpCons @ G @ A @ C ) @ ( c_Polynomial_Osmult @ G @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(2581,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(2497,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ B @ ( c_Polynomial_Osmult @ C @ A @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) ) )
= ( c_Polynomial_OpCons @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
thf(4540,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ B @ ( c_Polynomial_Osmult @ C @ A @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) ) )
= ( c_Polynomial_OpCons @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(705,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(3540,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(6416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
| ( ( c_Groups_Oplus__class_Oplus @ A @ v_a @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) )
| ( B != tc_Complex_Ocomplex ) ),
inference(paramod_ordered,[status(thm)],[1053,4558]) ).
thf(6417,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ B ) @ tc_Complex_Ocomplex @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ tc_Complex_Ocomplex ) )
| ( ( c_Groups_Oplus__class_Oplus @ A @ v_a @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[6416:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).
thf(6908,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ B ) @ tc_Complex_Ocomplex @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ tc_Complex_Ocomplex ) )
| ( ( c_Groups_Oplus__class_Oplus @ A @ v_a @ ( sk1 @ v_p ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[6417]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).
thf(3409,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Rings_Ocomm__ring @ D )
& ( class_Rings_Odvd @ D ) )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ! [E: $i,F: $i] :
( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
<=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( c_Groups_Otimes__class_Otimes @ D @ F @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
thf(4135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Rings_Ocomm__ring @ D )
& ( class_Rings_Odvd @ D ) )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ! [E: $i,F: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( c_Groups_Otimes__class_Otimes @ D @ F @ B ) ) @ A ) ) )
& ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( c_Groups_Otimes__class_Otimes @ D @ F @ B ) ) @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__le) ).
thf(3064,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(603,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse) ).
thf(3109,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
thf(1979,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(3215,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( D != C )
& ( B != A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(4361,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( D != C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ ( c_Polynomial_Odegree @ C @ B ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ A @ B )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__dvd__antisym) ).
thf(1525,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ ( c_Polynomial_Odegree @ C @ B ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ A @ B )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(3476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).
thf(2749,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(2788,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(1779,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Odegree @ B @ ( c_Polynomial_OpCons @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
thf(4081,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Odegree @ B @ ( c_Polynomial_OpCons @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
thf(3856,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
= A ) )
& ( ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
thf(1563,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(127,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
thf(1466,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
thf(4036,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
thf(2995,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(214,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
thf(1732,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1028,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
thf(4550,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
thf(1202,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(2203,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
thf(2546,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(4195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opoly__gcd @ D @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) )
= ( c_Polynomial_Opoly__gcd @ D @ B @ ( c_Polynomial_Opoly__gcd @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Oleft__commute) ).
thf(1286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opoly__gcd @ D @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) )
= ( c_Polynomial_Opoly__gcd @ D @ B @ ( c_Polynomial_Opoly__gcd @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(3321,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
<=> ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__poly__def) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
=> ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) )
& ( ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
| ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ),
inference(cnf,[status(esa)],[1033]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(2368,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ~ ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) )
= ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__monic) ).
thf(2440,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ~ ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) )
= ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(984,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
thf(4448,plain,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1663,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(621,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__synthetic__div) ).
thf(3190,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(190,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
thf(1648,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ! [D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__le) ).
thf(2001,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ! [D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ouminus @ B )
=> ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(1219,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ouminus @ B )
=> ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less2) ).
thf(1747,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1000,axiom,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
thf(4489,plain,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(2894,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( ( hAPP @ ( hAPP @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) @ B )
= B )
=> ( ( c_Polynomial_Opoly__rec @ A @ D @ B @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__rec__0) ).
thf(3707,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( ( hAPP @ ( hAPP @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) @ B )
= B )
=> ( ( c_Polynomial_Opoly__rec @ A @ D @ B @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(992,axiom,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
thf(4470,plain,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(4380,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
thf(1959,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(441,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
thf(2556,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
<=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
thf(1103,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
| ( B = A ) ) )
& ( ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
| ( B = A ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
thf(1548,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
thf(1927,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(3375,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).
thf(1595,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(4503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(3792,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(2376,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(4453,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(36,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
thf(1154,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(942,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(4341,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( class_Fields_Ofield @ H )
=> ( ( c_Polynomial_Opdivmod__rel @ H @ G @ F @ E @ D )
=> ( ( c_Polynomial_Opdivmod__rel @ H @ E @ C @ B @ A )
=> ( c_Polynomial_Opdivmod__rel @ H @ G @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ H ) @ F @ C ) @ B @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ H ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ H ) @ F @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__mult) ).
thf(3319,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( class_Fields_Ofield @ H )
=> ( ( c_Polynomial_Opdivmod__rel @ H @ G @ F @ E @ D )
=> ( ( c_Polynomial_Opdivmod__rel @ H @ E @ C @ B @ A )
=> ( c_Polynomial_Opdivmod__rel @ H @ G @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ H ) @ F @ C ) @ B @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ H ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ H ) @ F @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(1620,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(4122,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(514,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
thf(2806,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(518,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(2817,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Omonom @ C @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__monom__eq) ).
thf(1124,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Omonom @ C @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(2959,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(843,axiom,
! [A: $i] :
( ( c_Nat_Onat_Onat__size @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_Onat_Onat__size @ A ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
thf(4000,plain,
! [A: $i] :
( ( c_Nat_Onat_Onat__size @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_Onat_Onat__size @ A ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(3387,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(3547,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(1832,plain,
~ ? [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(miniscope,[status(thm)],[1831]) ).
thf(1833,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(cnf,[status(esa)],[1832]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
thf(4283,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Rings_Odvd__class_Odvd @ E @ D @ C )
=> ( ( c_Rings_Odvd__class_Odvd @ E @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
thf(1615,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Rings_Odvd__class_Odvd @ E @ D @ C )
=> ( ( c_Rings_Odvd__class_Odvd @ E @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
thf(1784,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(636,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).
thf(3255,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(2525,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(888,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(4157,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(4158,plain,
~ ? [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
inference(miniscope,[status(thm)],[4157]) ).
thf(4159,plain,
! [B: $i,A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
inference(cnf,[status(esa)],[4158]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(2849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) @ A )
= ( c_Polynomial_OpCons @ C @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__single) ).
thf(3758,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) @ A )
= ( c_Polynomial_OpCons @ C @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(827,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
thf(3945,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(2674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
& ( ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__right) ).
thf(2568,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(207,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
thf(1701,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(2398,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
= ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__minus__right) ).
thf(2695,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
= ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( ( D = B )
& ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__unique) ).
thf(1226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( ( D = B )
& ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
thf(1488,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(2827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(4505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(725,axiom,
! [A: $i] :
( ( class_Groups_Ogroup__add @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
thf(3599,plain,
! [A: $i] :
( ( class_Groups_Ogroup__add @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ A @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__1__right) ).
thf(3773,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ A @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(2220,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(3651,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(4149,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__diff__right) ).
thf(3594,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(2457,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(126,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
thf(1464,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(332,axiom,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(2148,plain,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(4526,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(4537,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(3022,plain,
! [A: $i] :
( ~ ( class_Rings_Ozero__neq__one @ A )
| ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(cnf,[status(esa)],[3021]) ).
thf(3023,plain,
! [A: $i] :
( ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) )
| ~ ( class_Rings_Ozero__neq__one @ A ) ),
inference(lifteq,[status(thm)],[3022]) ).
thf(343,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(2193,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(1786,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(767,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
thf(3726,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
thf(3077,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(740,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(3646,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
thf(4112,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( ( c_Polynomial_Oorder @ C @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).
thf(1635,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( ( c_Polynomial_Oorder @ C @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( ( c_Polynomial_Oorder @ C @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__diff__less) ).
thf(3002,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(3783,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Polynomial_Osmult @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__right) ).
thf(3487,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Polynomial_Osmult @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(2055,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
thf(1092,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(863,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
<=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(4060,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(2706,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(1765,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(730,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(3619,plain,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(922,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(4273,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__dvd1) ).
thf(1258,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(4245,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(53,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
thf(1224,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(380,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(2346,plain,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(2521,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(940,axiom,
class_Rings_Odvd @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
thf(4337,plain,
class_Rings_Odvd @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(909,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__add__positive) ).
thf(4228,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(2151,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(2383,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(2415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( c_Rings_Odvd__class_Odvd @ B @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
thf(1574,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( c_Rings_Odvd__class_Odvd @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
<=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(3287,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Groups_Oone__class_Oone @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1048,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ~ ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(cnf,[status(esa)],[1047]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(1722,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( ( C = B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Omonom @ D @ A @ C ) ) @ B )
= A ) )
& ( ( C != B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Omonom @ D @ A @ C ) ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__monom) ).
thf(2116,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( ( C = B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Omonom @ D @ A @ C ) ) @ B )
= A ) )
& ( ( C != B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Omonom @ D @ A @ C ) ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__power__le) ).
thf(2856,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(103,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
thf(1376,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(416,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__poly__def) ).
thf(2478,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(635,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(3251,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(3038,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
thf(1117,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
thf(1349,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(3270,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(2257,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(2284,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Polynomial_Osmult @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I1_J) ).
thf(1603,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Polynomial_Osmult @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(373,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(2299,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__minus) ).
thf(3106,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I2_J) ).
thf(1542,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ozero @ E )
=> ( ( ( c_Polynomial_OpCons @ E @ D @ C )
= ( c_Polynomial_OpCons @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
thf(1771,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ozero @ E )
=> ( ( ( ( c_Polynomial_OpCons @ E @ D @ C )
= ( c_Polynomial_OpCons @ E @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Polynomial_OpCons @ E @ D @ C )
= ( c_Polynomial_OpCons @ E @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(556,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
thf(2943,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
thf(3710,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(2945,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
| ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[1036]) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
| ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) ) ),
inference(lifteq,[status(thm)],[1039]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
inference(simp,[status(thm)],[1042]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ ( c_Polynomial_OpCons @ D @ A @ B ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
thf(3066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ ( c_Polynomial_OpCons @ D @ A @ B ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
thf(2896,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__minus) ).
thf(4477,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(612,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(3160,plain,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(310,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(2065,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__case @ D @ C @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(4388,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__case @ D @ C @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1664,plain,
! [A: $i] :
( ? [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(miniscope,[status(thm)],[1663]) ).
thf(1665,plain,
! [B: $i,A: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(cnf,[status(esa)],[1664]) ).
thf(1666,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(lifteq,[status(thm)],[1665]) ).
thf(1667,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(simp,[status(thm)],[1666]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(4203,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__poly__def) ).
thf(2182,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Oadd) ).
thf(4401,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).
thf(2742,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(457,axiom,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( ( c_Polynomial_Opoly__gcd @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__0__0) ).
thf(2610,plain,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( ( c_Polynomial_Opoly__gcd @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(4277,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(2410,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(452,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(2593,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Fields_Ofield @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( c_Polynomial_Opdivmod__rel @ F @ D @ C @ B @ A )
=> ( c_Polynomial_Opdivmod__rel @ F @ D @ ( c_Polynomial_Osmult @ F @ E @ C ) @ ( c_Polynomial_Osmult @ F @ ( c_Rings_Oinverse__class_Oinverse @ F @ E ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__right) ).
thf(1344,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Fields_Ofield @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( c_Polynomial_Opdivmod__rel @ F @ D @ C @ B @ A )
=> ( c_Polynomial_Opdivmod__rel @ F @ D @ ( c_Polynomial_Osmult @ F @ E @ C ) @ ( c_Polynomial_Osmult @ F @ ( c_Rings_Oinverse__class_Oinverse @ F @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
= ( c_Polynomial_OpCons @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__pCons) ).
thf(2553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
= ( c_Polynomial_OpCons @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
thf(1177,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(2974,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Omonom @ D @ C @ B ) @ ( c_Polynomial_Omonom @ D @ A @ B ) )
= ( c_Polynomial_Omonom @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__monom) ).
thf(2842,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Omonom @ D @ C @ B ) @ ( c_Polynomial_Omonom @ D @ A @ B ) )
= ( c_Polynomial_Omonom @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__less) ).
thf(2025,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1078,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Groups_Oordered__ab__group__add @ E )
| ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
!= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
| ~ ( c_Orderings_Oord__class_Oless @ E @ D @ C )
| ( c_Orderings_Oord__class_Oless @ E @ B @ A ) ),
inference(cnf,[status(esa)],[1076]) ).
thf(1080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
!= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
| ~ ( class_Groups_Oordered__ab__group__add @ E )
| ~ ( c_Orderings_Oord__class_Oless @ E @ D @ C )
| ( c_Orderings_Oord__class_Oless @ E @ B @ A ) ),
inference(lifteq,[status(thm)],[1078]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
thf(2632,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(4103,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(4009,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( c_Groups_Otimes__class_Otimes @ F @ E @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F @ E @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(2314,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( c_Groups_Otimes__class_Otimes @ F @ E @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ? [C: $i] :
( B
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
thf(2625,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [C: $i] :
( B
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) ) )
& ( ? [C: $i] :
( B
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(7291,plain,
! [A: $i] :
( ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) )
| ( ( class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex )
!= ( class_Rings_Ozero__neq__one @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4470,3023]) ).
thf(7292,plain,
( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(pattern_uni,[status(thm)],[7291:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).
thf(8102,plain,
! [A: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) )
| ( ( class_Rings_Olinordered__semidom @ tc_Nat_Onat )
!= ( class_Rings_Olinordered__semidom @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1382,1740]) ).
thf(8103,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(pattern_uni,[status(thm)],[8102:[bind(A,$thf( tc_Nat_Onat ))]]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( c_Polynomial_Osmult @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
thf(3800,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( c_Polynomial_Osmult @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( c_Polynomial_Osmult @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
thf(4264,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).
thf(1149,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
thf(3298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(2542,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opdivmod__rel @ D @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ B @ A )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).
thf(2289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( ( c_Polynomial_Opdivmod__rel @ D @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ B @ A )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A = C ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A = C ) )
=> ( c_Polynomial_Opdivmod__rel @ D @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__divide__inverse) ).
thf(2578,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(1171,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__mult__le) ).
thf(2418,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A )
= ( c_Polynomial_Osmult @ D @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__smult__left) ).
thf(2962,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A )
= ( c_Polynomial_Osmult @ D @ C @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_OpCons @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ B @ C ) @ ( c_Polynomial_OpCons @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
thf(2212,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_OpCons @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ B @ C ) @ ( c_Polynomial_OpCons @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).
thf(2086,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(1643,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_OpCons @ C @ A @ B ) )
= ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
thf(3674,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_OpCons @ C @ A @ B ) )
= ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
thf(2931,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(3953,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(2752,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(2022,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
thf(1250,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(2303,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mult) ).
thf(4497,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff) ).
thf(1474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(910,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(4232,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(395,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2401,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(676,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(3423,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(2481,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Osmult @ D @ B @ A ) )
= ( c_Polynomial_Osmult @ D @ B @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__smult__right) ).
thf(2620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ ( c_Polynomial_Osmult @ D @ B @ A ) )
= ( c_Polynomial_Osmult @ D @ B @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
thf(1445,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).
thf(1528,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(820,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD) ).
thf(3917,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ B @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(2139,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__1) ).
thf(3687,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(816,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
thf(3908,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
| ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
thf(3876,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
| ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
| ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ A )
<=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
thf(2984,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ A )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(1805,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(2506,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(690,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(3490,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(867,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ A ) @ ( c_Polynomial_OpCons @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
thf(4084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ A ) @ ( c_Polynomial_OpCons @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(1034,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ),
inference(cnf,[status(esa)],[1033]) ).
thf(961,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
thf(4394,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( c_Polynomial_Opdivmod__rel @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__0) ).
thf(1758,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( c_Polynomial_Opdivmod__rel @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
=> ( ( B = A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
thf(1208,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
=> ( ( B = A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1018,axiom,
class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
thf(4529,plain,
class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
thf(1277,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) )
& ( ( c_Rings_Odvd__class_Odvd @ C @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
thf(3278,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).
thf(1181,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(939,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(4336,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(4168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(2005,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
thf(1413,plain,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( c_Polynomial_Osmult @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Osmult @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__minus__right) ).
thf(4331,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( c_Polynomial_Osmult @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Osmult @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( c_Polynomial_Omonom @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
<=> ( B
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
thf(3009,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( ( c_Polynomial_Omonom @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Omonom @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(966,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(4405,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(5503,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) )
| ~ ( class_Rings_Olinordered__idom @ B )
| ( ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) )
!= ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5269,1048]) ).
thf(5507,plain,
! [B: $i,A: $i] :
( ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ~ ( class_Rings_Olinordered__idom @ A )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) )
| ~ ( class_Rings_Olinordered__idom @ B )
| ( A != B )
| ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(simp,[status(thm)],[5503]) ).
thf(5513,plain,
! [A: $i] :
( ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ~ ( class_Rings_Olinordered__idom @ A )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) )
| ~ ( class_Rings_Olinordered__idom @ A )
| ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(simp,[status(thm)],[5507]) ).
thf(5587,plain,
! [A: $i] :
( ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
| ~ ( class_Rings_Olinordered__idom @ A )
| ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
!= ( sk1 @ v_p ) )
| ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(simp,[status(thm)],[5513]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq) ).
thf(3193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opdivmod__rel @ D @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ C @ B @ A )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__0__iff) ).
thf(3427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( ( c_Polynomial_Opdivmod__rel @ D @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ C @ B @ A )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( c_Polynomial_Opdivmod__rel @ D @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Oinverse @ D @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ D @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Rings_Oinverse__class_Oinverse @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__inverse__lemma) ).
thf(4013,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Oinverse @ D @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ D @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Rings_Oinverse__class_Oinverse @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
thf(3576,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(2665,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A )
<=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
thf(2318,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A )
=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(3395,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(7297,plain,
! [A: $i] :
( ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) )
| ( ( class_Rings_Ozero__neq__one @ tc_Nat_Onat )
!= ( class_Rings_Ozero__neq__one @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3517,3023]) ).
thf(7298,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(pattern_uni,[status(thm)],[7297:[bind(A,$thf( tc_Nat_Onat ))]]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(3161,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(266,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
thf(1905,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
thf(4292,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).
thf(1509,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
thf(1081,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
thf(2927,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(858,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( ( c_Polynomial_Odegree @ A @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__1) ).
thf(4045,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( ( c_Polynomial_Odegree @ A @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(917,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).
thf(4255,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(951,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
thf(4360,plain,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(3913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Polynomial_Odegree @ C @ A ) )
=> ? [D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ D )
& ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__degree__imp) ).
thf(3754,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Polynomial_Odegree @ C @ A ) )
=> ? [D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ D )
& ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(799,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(3833,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
thf(3129,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(625,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__inverse) ).
thf(3209,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(807,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(3872,plain,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
thf(1531,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_OpCons @ D @ B @ A ) @ C )
= ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_OpCons @ D @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ A @ C ) ) @ ( c_Polynomial_Osmult @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_OpCons @ D @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ A @ C ) ) ) @ ( c_Polynomial_Odegree @ D @ C ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pCons) ).
thf(3608,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_OpCons @ D @ B @ A ) @ C )
= ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_OpCons @ D @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ A @ C ) ) @ ( c_Polynomial_Osmult @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_OpCons @ D @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ A @ C ) ) ) @ ( c_Polynomial_Odegree @ D @ C ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(540,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
thf(2882,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).
thf(2831,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(3640,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(534,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(2863,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(4490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(3112,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(2977,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse) ).
thf(1156,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
thf(1566,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__add__right) ).
thf(2012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__diff__le) ).
thf(1941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(4200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osmult @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__smult__le) ).
thf(2386,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osmult @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(2407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(787,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
thf(3786,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(67,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
thf(1267,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(633,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Odvd @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
thf(3246,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Odvd @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).
thf(2454,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).
thf(2688,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(550,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2920,plain,
! [A: $i] :
( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
thf(1186,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(3554,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_OpCons @ C @ B @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( c_Nat_Onat_Onat__case @ C @ B @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__def) ).
thf(1869,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_OpCons @ C @ B @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( c_Nat_Onat_Onat__case @ C @ B @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(583,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
thf(3026,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).
thf(1262,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(378,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(2337,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(4351,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(3828,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).
thf(3853,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ozero @ F )
=> ( ( ( hAPP @ ( hAPP @ ( hAPP @ E @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ F ) ) ) @ D )
= D )
=> ( ( c_Polynomial_Opoly__rec @ C @ F @ D @ E @ ( c_Polynomial_OpCons @ F @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ E @ B ) @ A ) @ ( c_Polynomial_Opoly__rec @ C @ F @ D @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
thf(3715,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ozero @ F )
=> ( ( ( hAPP @ ( hAPP @ ( hAPP @ E @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ F ) ) ) @ D )
= D )
=> ( ( c_Polynomial_Opoly__rec @ C @ F @ D @ E @ ( c_Polynomial_OpCons @ F @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ E @ B ) @ A ) @ ( c_Polynomial_Opoly__rec @ C @ F @ D @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Omonom @ C @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__monom__le) ).
thf(1499,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Omonom @ C @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(963,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(4398,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).
thf(2092,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(2165,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( B
= ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(3885,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( B
= ( c_Nat_OSuc @ A ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( B
= ( c_Nat_OSuc @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leading__coeff__0__iff) ).
thf(4003,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
| ( c_Polynomial_Opos__poly @ C @ A )
| ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ),
inference(cnf,[status(esa)],[1036]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
thf(2276,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(2128,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).
thf(1317,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(3127,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(913,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(4241,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__add) ).
thf(3847,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(3412,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(3174,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) @ A )
= ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__minus__left) ).
thf(2044,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) @ A )
= ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(4117,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(1579,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( B != A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
thf(1336,plain,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( B != A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
thf(3769,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(355,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
thf(2247,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(2500,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(1849,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(3124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
= ( c_Nat_Onat_Onat__case @ C @ B @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__pCons) ).
thf(1802,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
= ( c_Nat_Onat_Onat__case @ C @ B @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(2379,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__diff) ).
thf(4436,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).
thf(1506,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
thf(1504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(3024,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
= ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
<=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(3961,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
= ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
= ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(968,axiom,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
thf(4414,plain,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(442,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(2558,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(834,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(3970,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(2113,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
thf(3415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Divides_Oring__div @ F )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ E @ D )
= ( c_Divides_Odiv__class_Omod @ F @ C @ D ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ B @ D )
= ( c_Divides_Odiv__class_Omod @ F @ A @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D )
= ( c_Divides_Odiv__class_Omod @ F @ ( c_Groups_Ominus__class_Ominus @ F @ C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
thf(1221,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Divides_Oring__div @ F )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ E @ D )
= ( c_Divides_Odiv__class_Omod @ F @ C @ D ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ B @ D )
= ( c_Divides_Odiv__class_Omod @ F @ A @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D )
= ( c_Divides_Odiv__class_Omod @ F @ ( c_Groups_Ominus__class_Ominus @ F @ C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(999,axiom,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
thf(4488,plain,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(367,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
thf(2279,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1008,axiom,
class_Groups_Ominus @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
thf(4510,plain,
class_Groups_Ominus @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(4698,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
| ( c_Polynomial_Opos__poly @ C @ A )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
!= ( sk1 @ v_p ) )
| ( A
!= ( sk1 @ v_p ) ) ),
inference(paramod_ordered,[status(thm)],[1041,4558]) ).
thf(4699,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( sk1 @ v_p ) ) )
| ( c_Polynomial_Opos__poly @ B @ ( sk1 @ v_p ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[4698:[bind(A,$thf( sk1 @ v_p )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4748,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( sk1 @ v_p ) ) )
| ( c_Polynomial_Opos__poly @ B @ ( sk1 @ v_p ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
!= ( sk1 @ v_p ) ) ),
inference(simp,[status(thm)],[4699]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ A ) @ ( c_Polynomial_Osmult @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__add__left) ).
thf(2145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ A ) @ ( c_Polynomial_Osmult @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
thf(4143,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(4235,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
thf(1585,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).
thf(1094,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
thf(1140,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
thf(2728,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(921,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
thf(4267,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) )
& ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
thf(4225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(943,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__add) ).
thf(4342,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(101,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(1372,plain,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).
thf(2892,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(3007,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1014,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(4516,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(668,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(3398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).
thf(1240,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__divide) ).
thf(1617,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__le) ).
thf(2875,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(927,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(4289,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(3620,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(975,axiom,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(4424,plain,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__divide) ).
thf(1685,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
thf(1553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
thf(1844,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(3188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(2347,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(2215,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(4185,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(3625,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(3665,plain,
( ( c_Nat_Onat_Onat__size @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(lifteq,[status(thm)],[3664]) ).
thf(291,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(1998,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
thf(2435,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ B ) )
& ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(644,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(3284,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(669,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
thf(3400,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).
thf(3478,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(1949,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(890,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(4165,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(4419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
thf(1321,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1834,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).
thf(1913,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_OpCons @ C @ A @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_OpCons @ C @ A @ B ) )
= ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__eq__if) ).
thf(2490,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_OpCons @ C @ A @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_OpCons @ C @ A @ B ) )
= ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( B
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(2110,plain,
! [A: $i,B: $i] :
( ( B
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
thf(1390,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(892,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
thf(4170,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(4463,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(74,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
thf(1289,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(123,axiom,
! [A: $i] :
( ( class_Fields_Ofield__inverse__zero @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
thf(1453,plain,
! [A: $i] :
( ( class_Fields_Ofield__inverse__zero @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
= ( c_Polynomial_OpCons @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pCons) ).
thf(1866,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
= ( c_Polynomial_OpCons @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(2071,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
thf(2658,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ A )
= ( c_Power_Opower__class_Opower @ D @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(2775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ A )
= ( c_Power_Opower__class_Opower @ D @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).
thf(1734,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(2792,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
thf(1326,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
<=> ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
thf(1253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(1341,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(4042,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).
thf(1745,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Omonom @ C @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Polynomial_OpCons @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Polynomial_Omonom @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__Suc) ).
thf(2971,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Omonom @ C @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Polynomial_OpCons @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Polynomial_Omonom @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
thf(3561,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).
thf(3331,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(919,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
thf(4261,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(337,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero) ).
thf(2167,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(2273,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) )
<=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(2174,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).
thf(1476,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
thf(2251,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Opcompose @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_OpCons @ D @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ A @ ( c_Polynomial_Opcompose @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
thf(3825,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Opcompose @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_OpCons @ D @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ A @ ( c_Polynomial_Opcompose @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(2811,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(601,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
thf(3104,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(774,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3748,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(734,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(3630,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(252,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
<=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(1854,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) )
& ( ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Power_Opower__class_Opower @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__power) ).
thf(4338,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Power_Opower__class_Opower @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
thf(1523,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Polynomial_Osmult @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__1__left) ).
thf(2130,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Polynomial_Osmult @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(159,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
thf(1558,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(2934,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2262,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
thf(1861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Omonom @ D @ C @ B ) @ ( c_Polynomial_Omonom @ D @ A @ B ) )
= ( c_Polynomial_Omonom @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__monom) ).
thf(2475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Omonom @ D @ C @ B ) @ ( c_Polynomial_Omonom @ D @ A @ B ) )
= ( c_Polynomial_Omonom @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B = A )
<=> ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ D )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__poly__eq) ).
thf(4214,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( B = A )
=> ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ D )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) )
& ( ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ D )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(311,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
thf(2066,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Polynomial_Osmult @ D @ B @ A ) )
= ( c_Polynomial_Osmult @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__smult) ).
thf(2680,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osmult @ D @ C @ ( c_Polynomial_Osmult @ D @ B @ A ) )
= ( c_Polynomial_Osmult @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(965,axiom,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
thf(4404,plain,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(1513,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(4306,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
= A ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
= A )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
thf(2019,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(675,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(3420,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd) ).
thf(2956,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ C @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(467,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(2648,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(722,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(3585,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(640,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(3267,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
thf(1294,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Rings_Odvd @ C )
& ( class_Rings_Osemiring__0 @ C ) )
=> ( ? [D: $i] : ( hBOOL @ ( hAPP @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ D ) ) )
<=> ? [D: $i] :
( ( c_Rings_Odvd__class_Odvd @ C @ A @ ( c_Groups_Oplus__class_Oplus @ C @ D @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
thf(3677,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Rings_Odvd @ C )
& ( class_Rings_Osemiring__0 @ C ) )
=> ( ( ? [D: $i] : ( hBOOL @ ( hAPP @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ D ) ) )
=> ? [D: $i] :
( ( c_Rings_Odvd__class_Odvd @ C @ A @ ( c_Groups_Oplus__class_Oplus @ C @ D @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( c_Rings_Odvd__class_Odvd @ C @ A @ ( c_Groups_Oplus__class_Oplus @ C @ D @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(2162,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(2917,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(2623,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(3761,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(4039,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(875,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Polynomial_Odegree @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) )
= ( c_Polynomial_Odegree @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__minus) ).
thf(4114,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Polynomial_Odegree @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) )
= ( c_Polynomial_Odegree @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(949,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(4356,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(2719,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(3733,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(639,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(3264,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(4523,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(789,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
thf(3790,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(1480,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(683,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
thf(3469,plain,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(841,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
thf(3992,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(2142,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__0 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_Omonom @ E @ D @ C ) @ ( c_Polynomial_Omonom @ E @ B @ A ) )
= ( c_Polynomial_Omonom @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__monom) ).
thf(3658,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__0 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_Omonom @ E @ D @ C ) @ ( c_Polynomial_Omonom @ E @ B @ A ) )
= ( c_Polynomial_Omonom @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(2218,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__reduce) ).
thf(1133,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(426,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
thf(2517,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Polynomial_Odegree @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__degree) ).
thf(2683,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Polynomial_Odegree @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(1725,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
thf(1280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
thf(1678,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(3511,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult2) ).
thf(1395,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).
thf(1625,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(3373,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult) ).
thf(1593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(3464,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(6412,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
| ( c_Polynomial_Opos__poly @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
| ( A
!= ( sk1 @ v_p ) )
| ( B
!= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) ),
inference(paramod_ordered,[status(thm)],[1053,4558]) ).
thf(6413,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) @ A )
| ( c_Polynomial_Opos__poly @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) )
| ( A
!= ( sk1 @ v_p ) ) ),
inference(pattern_uni,[status(thm)],[6412:[bind(A,$thf( A )),bind(B,$thf( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) )),bind(C,$thf( C ))]]) ).
thf(6906,plain,
! [A: $i] :
( ~ ( class_Rings_Olinordered__idom @ A )
| ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) @ ( sk1 @ v_p ) )
| ( c_Polynomial_Opos__poly @ A @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ A ) @ ( sk1 @ v_p ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) ) ) ),
inference(simp,[status(thm)],[6413]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
thf(2050,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(950,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(4357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__left) ).
thf(3496,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
thf(3015,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(1855,plain,
( ! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) )
& ! [A: $i] :
( ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
inference(miniscope,[status(thm)],[1854]) ).
thf(1856,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_Nat_OSuc @ B ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
inference(cnf,[status(esa)],[1855]) ).
thf(1858,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_Nat_OSuc @ B ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
inference(lifteq,[status(thm)],[1856]) ).
thf(1859,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
inference(simp,[status(thm)],[1858]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
thf(3956,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(895,axiom,
! [A: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
thf(4178,plain,
! [A: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).
thf(1657,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(925,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ ( c_Nat_OSuc @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(4281,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ ( c_Nat_OSuc @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(712,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
thf(3558,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(3177,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pCons) ).
thf(4474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(2746,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(802,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
= ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mod__minus__right) ).
thf(3850,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
= ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Polynomial_Opos__poly @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__def) ).
thf(1410,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Polynomial_Opos__poly @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) )
=> ( c_Polynomial_Opos__poly @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(2366,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2404,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(677,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(3426,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(4193,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__eq__left) ).
thf(2668,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(3506,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(2783,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__field @ F )
=> ( ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ ( c_Groups_Otimes__class_Otimes @ F @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).
thf(3822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__field @ F )
=> ( ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ ( c_Groups_Otimes__class_Otimes @ F @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
thf(3145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(4303,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(3897,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(4024,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(1789,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(219,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(1742,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(2549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).
thf(2241,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( B = A )
<=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
thf(2731,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(1827,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).
thf(1378,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
& ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opoly__gcd @ D @ ( c_Polynomial_Opoly__gcd @ D @ C @ B ) @ A )
= ( c_Polynomial_Opoly__gcd @ D @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Oassoc) ).
thf(1357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opoly__gcd @ D @ ( c_Polynomial_Opoly__gcd @ D @ C @ B ) @ A )
= ( c_Polynomial_Opoly__gcd @ D @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
thf(3392,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
thf(3939,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).
thf(1902,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_Osmult @ D @ C @ B ) ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__smult) ).
thf(4345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_Osmult @ D @ C @ B ) ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mod__minus__left) ).
thf(2270,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(274,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(1930,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(2353,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1977,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
thf(1129,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__le) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(3701,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Osmult @ D @ C @ B ) ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__smult) ).
thf(2803,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Osmult @ D @ C @ B ) ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(914,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
thf(4242,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(2600,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(547,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
thf(2898,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( c_Polynomial_Osmult @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ A ) @ ( c_Polynomial_Osmult @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__diff__left) ).
thf(3570,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( c_Polynomial_Osmult @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Polynomial_Osmult @ D @ C @ A ) @ ( c_Polynomial_Osmult @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( ( c_Divides_Odiv__class_Omod @ D @ C @ B )
= ( c_Divides_Odiv__class_Omod @ D @ A @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ouminus__class_Ouminus @ D @ C ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ouminus__class_Ouminus @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__cong) ).
thf(1537,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( ( c_Divides_Odiv__class_Omod @ D @ C @ B )
= ( c_Divides_Odiv__class_Omod @ D @ A @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ouminus__class_Ouminus @ D @ C ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ ( c_Groups_Ouminus__class_Ouminus @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(727,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(3605,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(169,axiom,
! [A: $i] :
( ( class_Groups_Osgn__if @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).
thf(1582,plain,
! [A: $i] :
( ( class_Groups_Osgn__if @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
thf(2265,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
thf(3869,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(4206,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(1925,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).
thf(1597,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(3740,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ozero) ).
thf(1880,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(4019,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Oring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__eq) ).
thf(1299,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Oring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(2484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
| ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
thf(3812,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
| ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
| ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(4533,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(829,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(3950,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(720,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
thf(3580,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
= ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__pCons) ).
thf(1962,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
= ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).
thf(3212,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
thf(1449,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(709,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(3553,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(128,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
thf(1468,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(3035,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(3669,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__pos) ).
thf(1331,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(178,axiom,
! [A: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__zero) ).
thf(1606,plain,
! [A: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Oone__class_Oone @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__unique) ).
thf(3528,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Oone__class_Oone @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(938,axiom,
class_Groups_Oone @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
thf(4335,plain,
class_Groups_Oone @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1653,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(3227,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(99,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
thf(1367,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(4555,plain,
! [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
!= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_p ) )
| ( ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A )
!= ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) )
| ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ A ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[1032]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(3096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
<=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(2206,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) )
& ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(200,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(1681,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( c_Polynomial_Osmult @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Osmult @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__minus__left) ).
thf(2887,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( c_Polynomial_Osmult @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Osmult @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( c_Rings_Odvd__class_Odvd @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
thf(1184,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( c_Rings_Odvd__class_Odvd @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(2074,plain,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
thf(1490,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(4646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ C )
| ~ ( c_Polynomial_Opos__poly @ C @ ( c_Polynomial_OpCons @ C @ B @ A ) )
| ( c_Polynomial_Opos__poly @ C @ A )
| ( ( hAPP @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) )
| ( A
!= ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) ) ),
inference(paramod_ordered,[status(thm)],[1041,4557]) ).
thf(4647,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) ) )
| ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) )
| ( ( hAPP @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) ) ),
inference(pattern_uni,[status(thm)],[4646:[bind(A,$thf( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4752,plain,
! [B: $i,A: $i] :
( ~ ( class_Rings_Olinordered__idom @ B )
| ~ ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_OpCons @ B @ A @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) ) )
| ( c_Polynomial_Opos__poly @ B @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) )
| ( ( hAPP @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_a @ ( sk1 @ v_p ) ) )
!= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( sk1 @ v_p ) ) ) ),
inference(simp,[status(thm)],[4647]) ).
thf(372,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
thf(2297,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(861,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(4056,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(3052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(15,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(1088,plain,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(338,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
thf(2170,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(2834,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
thf(3721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(894,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(4174,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(929,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(4298,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A ) )
= ( c_Polynomial_Odegree @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
thf(2655,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A ) )
= ( c_Polynomial_Odegree @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(176722,plain,
$false,
inference(cvc4,[status(thm)],[1501,4447,3883,4094,2778,3661,3666,1982,2559,2544,1818,1956,3172,2199,3021,1036,3873,4188,2744,1369,4450,2341,2412,1237,3698,3979,2463,1899,3863,2595,1158,3072,2940,2381,2395,1591,2837,1305,4487,1041,2363,2077,3534,3317,4500,4515,3905,1522,1808,3417,3509,3285,2527,4391,2953,1401,1422,2947,1569,2671,3910,1793,2854,1692,4408,1486,4105,1671,1655,1872,4279,4440,3693,1919,4435,1458,1497,4543,3049,3745,4418,2607,2686,3004,2035,3367,3942,4011,3649,3135,4097,3365,2740,4110,4220,2448,11917,1260,4058,3370,1196,3236,3545,1046,1601,4198,4030,3809,1967,4467,2869,4511,2432,3994,1243,1127,3915,1782,4496,1576,4079,11568,6904,1935,3947,1650,3730,1645,4322,2819,5269,2136,1703,1623,3597,2654,3976,1430,2814,4151,3046,4415,1907,3148,3485,3776,1577,2562,2466,3248,1055,4238,3204,4439,3221,3029,4348,2698,1760,1660,2755,3495,1264,4334,1313,4349,4428,1059,3043,2571,3713,3099,4353,3638,1319,2767,1609,1741,4551,4141,2989,1100,1847,1545,2420,1922,2691,4119,3517,3840,3385,6905,1147,2373,3919,1347,1572,2635,3470,4383,1815,4460,3180,4471,4507,3602,1875,4514,2388,3268,3258,4756,3788,5792,2950,1946,3075,2259,2451,3973,1151,2540,1283,2017,1302,2794,4329,2027,4258,1373,3724,1040,1632,3163,2650,1334,3473,3983,2880,1682,3438,4050,2122,3525,1864,1383,2254,3923,3300,1051,3771,3389,3986,1169,3537,2190,3157,2286,2103,1943,4211,3492,4033,2618,2281,2861,1215,3685,1886,1072,2530,2523,1796,1119,4087,2979,3361,4536,3243,2809,2965,4519,4379,1697,1696,2586,2982,2884,3435,3582,4480,4531,4557,2047,1470,2641,1074,3899,3567,1691,3531,3635,4076,4370,2737,1311,3054,1736,2496,4312,2790,2660,1768,3550,4172,2773,1047,1730,1057,1274,1387,3261,4466,4016,2249,2541,1355,2133,1217,2937,4449,1824,2032,2890,1519,4397,3742,2969,4128,3069,4160,3664,11191,3207,3682,4021,3778,2015,1883,1560,4140,1365,5465,3578,4746,1836,1079,1407,3763,3727,1291,3166,3958,1938,2758,1032,3980,3403,2565,2663,1555,4155,3314,3499,3750,3556,2872,4385,1888,3718,3894,2068,4417,3926,3931,1740,1910,4027,4316,1360,3467,1762,1328,3632,1755,2638,2268,1089,3782,1234,3831,2840,1143,1270,1851,5270,2801,1534,4512,5345,4248,1121,4486,2709,1970,3218,4048,4544,1096,2509,3102,1540,3518,1878,2726,1138,2724,1719,2858,2537,3018,1397,3326,12179,2830,1075,4545,1612,3294,2460,1493,3311,2877,1739,4425,4421,1424,2312,2053,2196,4191,4513,1700,2613,1791,2172,2108,2038,2551,3671,3643,4444,3573,12314,2781,4530,1419,1451,1668,1932,3819,1799,3628,4416,3703,2968,1324,1114,3611,3656,2125,3654,1588,1478,1249,2519,4384,1456,1382,2487,2845,2598,1831,1231,2153,2900,2851,2243,2581,1060,2497,4540,3540,6908,3409,4135,3064,4152,3109,1979,3215,4361,1525,3476,2749,2788,1779,4081,1695,3856,1563,1466,4036,2995,2423,1732,4550,1202,2203,2546,4195,1286,3321,1035,2368,2440,4448,1663,3190,1648,2001,1219,1747,4489,2894,3707,1727,4470,4380,1959,2556,1103,1548,1927,3375,1595,4503,3792,2376,4453,1154,4341,3319,2225,1620,4122,2806,1965,2817,1124,2959,4000,3387,3547,1833,4283,1615,1784,3255,2525,4159,2849,3758,3945,2674,2568,1701,2398,2695,1226,1488,2827,4505,3599,3773,2220,3651,4149,1058,3594,2457,1464,2148,4526,4537,3023,4558,2193,1786,3726,3077,3646,4112,1635,3002,3783,3487,2055,1092,4060,2706,1765,3619,4273,1258,4245,1224,2346,2521,4337,4228,2151,2383,2415,1574,3287,1048,1722,2116,2856,1376,2478,3251,3038,1117,1349,3270,2257,2284,1603,2299,3106,1542,1771,2943,3710,2945,1043,4154,3066,2896,4477,3160,2065,4388,1667,4203,2182,4401,2742,2610,4277,2410,2593,1344,2553,1177,2974,2842,2025,1080,2632,4103,4009,2314,2625,7292,8103,3800,4264,1149,3298,2542,2289,2578,1688,1171,2418,2962,2212,2086,1643,3674,2931,3953,2752,2022,1250,2303,4497,1474,4232,2725,2401,3423,1044,2481,2620,1445,1528,11102,3917,2139,3687,3908,3876,2984,1805,2506,3490,4084,1034,4394,1758,1208,4529,1277,3278,1181,4336,4168,1049,2005,1413,1076,4331,3009,4405,5587,3193,3427,4013,3576,2665,2318,3395,2652,7298,3161,1905,4292,1509,1081,2927,4045,4255,4360,3913,3754,3833,3129,3209,3872,1531,3608,2882,2831,3640,2863,4490,3112,2977,1156,1566,2012,1941,4200,2386,2407,3786,1267,3246,2454,2688,2920,1186,3554,1869,3026,1262,2337,4351,3828,3853,3715,1053,1499,4398,2092,2165,3885,4003,1038,2276,2128,1317,3127,4241,3847,3412,3564,3174,2044,4117,1579,1336,3769,2247,2500,1849,3124,1802,2379,4436,1506,1504,3024,3961,4414,2558,3970,2113,3415,1221,4488,2279,4510,4748,2145,1749,4143,4235,1585,1094,1140,2728,4267,4225,4342,1372,2892,3007,4516,2584,3398,1240,1617,2875,4289,3620,4424,8987,1685,1553,1844,3188,2347,2215,4185,3625,3665,1998,2435,3284,3400,3478,1949,4165,4419,1321,1834,1913,2490,1189,2110,1390,4170,4463,1289,1453,1866,2071,2658,2775,1734,2792,1326,1253,1341,4042,1745,2971,3561,3331,3780,4261,2167,2273,2174,1476,2251,3825,2811,3104,3748,3630,1854,4338,1523,2130,1558,2934,2262,1861,2475,2041,4214,2066,2680,4404,1513,4306,2019,3420,1030,2956,2648,3585,3267,1294,3677,2162,2917,2623,3761,4039,4114,4356,2719,3733,3264,4523,3790,1480,3469,3992,2142,3658,2218,1133,2517,2683,1725,1280,1678,3511,1395,1625,3373,1593,3464,6906,2050,4357,3496,3015,1859,3956,4178,1657,4281,3558,3177,4474,2746,3850,1410,2366,1033,2404,3426,4193,2668,3506,2783,3822,3145,4303,3897,4157,4024,1056,1789,1742,2549,2241,2731,1827,1378,1357,3392,3939,1902,4345,2270,1930,2353,1829,1977,1129,2430,3701,2803,4242,2600,2898,3570,1537,1384,3605,1582,2265,3869,4206,1925,1597,3740,1880,4019,1299,2484,3812,4533,3950,3580,1962,3212,1449,3553,1468,3035,3669,1331,1606,3528,4335,1653,3227,1367,4555,3096,2206,1681,2887,1184,2074,1490,4752,2297,4056,3052,1088,2170,2834,3721,4174,1069,4298,2655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW189+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n021.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 : Thu May 18 22:42:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.83/1.11 % [INFO] Parsing done (263ms).
% 1.83/1.12 % [INFO] Running in sequential loop mode.
% 2.40/1.32 % [INFO] eprover registered as external prover.
% 2.40/1.32 % [INFO] cvc4 registered as external prover.
% 2.40/1.32 % [INFO] Scanning for conjecture ...
% 2.89/1.45 % [INFO] Found a conjecture and 1149 axioms. Running axiom selection ...
% 3.58/1.65 % [INFO] Axiom selection finished. Selected 1027 axioms (removed 122 axioms).
% 4.94/1.99 % [INFO] Problem is first-order (TPTP FOF).
% 4.94/2.02 % [INFO] Type checking passed.
% 4.94/2.02 % [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 ...
% 298.78/60.72 % External prover 'cvc4' found a proof!
% 298.78/60.72 % [INFO] Killing All external provers ...
% 298.78/60.73 % Time passed: 60204ms (effective reasoning time: 59602ms)
% 298.78/60.73 % 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)>
% 298.78/60.76 % Axioms used in derivation (1027): fact_zero__le__divide__iff, fact_dvd_Oord__less__eq__trans, fact_minus__monom, fact_le__SucI, fact_smult__minus__left, fact_dvd__imp__degree__le, fact_le__imp__diff__is__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_dvd_Oless__trans, fact_neg__le__0__iff__le, arity_Complex__Ocomplex__Rings_Odvd, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_Nat_Oadd__0__right, fact_degree__pcompose__le, fact_one__dvd, fact_right__inverse__eq, fact_real__squared__diff__one__factored, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, arity_Polynomial__Opoly__Rings_Osemiring__0, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, fact_coeff__pCons__0, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_neg__le__divide__eq, arity_Complex__Ocomplex__Groups_Omonoid__add, fact_pdivmod__rel__mult, fact_pos__add__strict, fact_mult__poly__0__right, fact_nonzero__inverse__inverse__eq, fact_add__strict__right__mono, fact_mult__1__left, fact_diff__0__eq__0, fact_minus__mult__left, fact_neg__divide__le__eq, fact_dvd__mult__cancel__left, fact_neg__equal__0__iff__equal, fact_inf__period_I4_J, fact_diff__add__inverse, fact_dvdI, fact_le__eq__less__or__eq, fact_minus__mult__right, fact_degree__smult__le, fact_trans__less__add1, fact_dvd_Oorder__trans, fact_add__poly__code_I2_J, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_comm__monoid_Ocomm__neutral, fact_inverse__1, fact_pdivmod__rel__unique__div, fact_le__degree, fact_order, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_mult__nonpos__nonpos, fact_dvd_Oeq__iff, fact_less__imp__inverse__less, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_degree__add__eq__right, fact_mult__left_Ominus, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_divide__nonpos__neg, fact_one__is__add, fact_diff__le__mono2, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_termination__basic__simps_I5_J, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, fact_mult__nonneg__nonpos, fact_poly__eq__0__iff__dvd, fact_mult__eq__0__iff, fact_less__imp__le__nat, fact_combine__common__factor, fact_split__mult__neg__le, fact_poly__gcd__greatest, fact_n__less__m__mult__n, fact_inverse__inverse__eq, fact_unity__coeff__ex, fact_Suc__mono, fact_one__less__inverse__iff, fact_nat_Osize_I4_J, fact_add__less__mono, fact_mult__le__less__imp__less, fact_mult__pCons__right, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_smult__dvd__cancel, fact_mult__right__less__imp__less, fact_positive__imp__inverse__positive, fact_dvd__triv__right, fact_add__leD1, fact_dvd_Oless__asym_H, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_Suc__times__mod__eq, fact_inverse__add, arity_Nat__Onat__Rings_Ocomm__semiring__0, fact_psize__eq__0__iff, fact_inverse__negative__iff__negative, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, arity_Nat__Onat__Groups_Omonoid__mult, fact_diff__Suc__less, fact_divide__inverse, fact_mult__0, fact_inverse__zero__imp__zero, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_dvd_Oless__imp__not__less, fact_add__right__imp__eq, fact_zero__less__diff, fact_nonzero__inverse__eq__imp__eq, fact_mult__mono, fact_neg__0__less__iff__less, fact_Suc__le__mono, fact_dvd__smult, fact_mult__poly__0__left, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_semigroup_Oassoc, fact_diff__diff__cancel, fact_nat__add__right__cancel, fact_neg__le__iff__le, fact_gr0__conv__Suc, arity_Polynomial__Opoly__Groups_Ominus, fact_coeff__eq__0, fact_poly__dvd__antisym, fact_inverse__zero, fact_dvd_Oord__eq__less__trans, fact_mult__le__mono2, fact_Suc__diff__diff, fact_mod__diff__cong, fact_smult__smult, fact_zero__le__one, fact_nat__add__left__cancel__less, fact_le__minus__iff, fact_pos__le__divide__eq, fact_mod__mult__distrib2, fact_coeff__inverse, fact_mult__imp__le__div__pos, fact_mod__less, fact_coeff__add, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_le__add__iff2, help_c__fequal__2, fact_mult__eq__self__implies__10, fact_minus__pCons, fact_poly__mod__minus__left, fact_le__neq__implies__less, fact_mult__left__le__imp__le, fact_divide__pos__neg, fact_minus__add__cancel, fact_add__pos__nonneg, fact_dvd__diffD, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_poly__add, fact_degree__pCons__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_add__strict__increasing2, fact_inverse__positive__imp__positive, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_linorder__neqE__linordered__idom, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, fact_mod__if, arity_Polynomial__Opoly__Rings_Olinordered__semidom, fact_smult__1__left, fact_sum__squares__le__zero__iff, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, fact_mult__smult__right, fact_smult__pCons, fact_synthetic__div__correct_H, fact_neg__less__0__iff__less, fact_divide__right__mono, fact_order__degree, fact_divide__1, fact_mult__strict__left__mono, fact_mod__mult__self4, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_sum__squares__ge__zero, fact_add__increasing2, fact_dvd__reduce, fact_zero__le__mult__iff, fact_synthetic__div__0, fact_divide__le__eq, fact_add__nonneg__eq__0__iff, fact_pdivmod__rel__by__0, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_mult_Ozero__left, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_poly__0, fact_add__mono, fact_coeff__1, fact_add__0__iff, fact_poly__smult, fact_add__right__mono, arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, fact_degree__1, fact_even__less__0__iff, fact_sgn__neg, fact_add__monom, fact_add__0__left, fact_gr0I, fact_sgn__minus, fact_add__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_minus__add, fact_divide__eq__imp, fact_nat__dvd__not__less, fact_leading__coeff__neq__0, arity_Nat__Onat__Rings_Osemiring__0, fact_diff__le__self, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, fact_mult__eq__1__iff, fact_smult__add__right, fact_degree__pCons__eq__if, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_divide__add__eq__iff, fact_less__add__eq__less, fact_nat__mult__1__right, arity_Complex__Ocomplex__Rings_Osemiring__0, arity_Complex__Ocomplex__Fields_Ofield, fact_inverse__less__imp__less, fact_poly__gcd_Oassoc, fact_mult__right_Odiff, fact_termination__basic__simps_I4_J, fact_le__iff__add, fact_one__reorient, fact_diff__commute, fact_minus__less__iff, arity_fun__Groups_Ouminus, fact_negative__imp__inverse__negative, fact_diff__Suc__eq__diff__pred, fact_divide__strict__left__mono__neg, fact_mod__1, fact_minus__mult__commute, arity_Polynomial__Opoly__Groups_Omonoid__add, fact_division__ring__inverse__add, fact_mult__left_Odiff, fact_eq__iff__diff__eq__0, fact_add__lessD1, fact_add__le__mono1, fact_poly__gcd__monic, fact_less__eq__nat_Osimps_I1_J, fact_less__degree__imp, fact_compl__mono, arity_Polynomial__Opoly__Int_Oring__char__0, fact_lessI, fact_zero__le__square, fact_dvd_Oantisym__conv, fact_zero__reorient, fact_dvd__0__right, fact_minus__divide__divide, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, arity_Polynomial__Opoly__Rings_Oring__1, fact_mult__less__mono1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_poly__mult, fact_split__mult__pos__le, fact_offset__poly__pCons, fact_minus__le__iff, fact_dvd__mult__cancel2, fact_nat_Oinject, fact_mult__left__le__one__le, fact_not__add__less2, fact_dvd__trans, fact_less__or__eq__imp__le, fact_Suc__less__SucD, fact_dvd_Oeq__refl, arity_Polynomial__Opoly__Groups_Osgn__if, fact_sgn__zero, fact_field__divide__inverse, fact_synthetic__div__pCons, arity_Complex__Ocomplex__RealVector_Oreal__field, fact_minus__apply, fact_inverse__le__1__iff, fact_add__0__right, fact_mult__pos__neg, fact_pos__less__divide__eq, fact_dvd_Oord__eq__le__trans, fact_nat__eq__add__iff2, fact_Suc__leI, fact_add__neg__nonpos, fact_sgn__mult, fact_diff__less, fact_mult__pos__neg2, fact_convex__bound__lt, fact_diff__is__0__eq_H, fact_DERIV__inverse__lemma, fact_nonzero__inverse__mult__distrib, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_less__irrefl__nat, fact_mod__smult__right, fact_mult_Oprod__diff__prod, fact_mod__diff__right__eq, fact_Suc__lessD, fact_Suc__n__not__le__n, fact_pdivmod__rel__0__iff, fact_not__less__less__Suc__eq, fact_diff__def, fact_dvd__mult2, fact_nat__mult__1, fact_mult__right__mono__neg, fact_diff__pCons, fact_divide__strict__right__mono__neg, fact_le__add2, fact_minus__divide__right, fact_dvd_Oless__imp__neq, fact_diff__self, fact_minus__nat_Odiff__0, arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_pos__divide__le__eq, fact_add__diff__assoc, fact_diff__0, fact_add__left__imp__eq, fact_poly__gcd__minus__right, fact_divide__left__mono__neg, fact_add__leD2, fact_mult__mono_H, fact_inverse__less__1__iff, fact_offset__poly__single, fact_poly__gcd__dvd2, fact_sgn__less, fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_not__less0, fact_monom__Suc, fact_trans__less__add2, fact_poly__offset__poly, fact_less__Suc__eq__le, arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, fact_nat__diff__split, fact_add__frac__eq, fact_mod__less__divisor, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_pcompose__0, fact_degree__pCons__le, arity_Complex__Ocomplex__Groups_Oab__semigroup__add, arity_Complex__Ocomplex__Fields_Ofield__inverse__zero, fact_divide__left__mono, fact_dvd_Oless__asym, fact_offset__poly__0, fact_inverse__divide, arity_Nat__Onat__Rings_Ocomm__semiring__1, fact_divide_Ominus, arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, fact_mod__pCons, fact_smult__diff__right, fact_synthetic__div__correct, fact_degree__smult__eq, fact_one__le__mult__iff, fact_not__less__eq, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, fact_mult__imp__div__pos__less, fact_nat_Osimps_I2_J, fact_mult__divide__mult__cancel__left, fact_zero__le__double__add__iff__zero__le__single__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_pCons__0__0, fact_degree__diff__le, fact_coeff__minus, fact_neg__less__iff__less, arity_Complex__Ocomplex__Rings_Osemiring, fact_pdivmod__rel__smult__right, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_minus__zero, arity_Complex__Ocomplex__Groups_Ogroup__add, fact_not__one__less__zero, fact_mult__le__cancel1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, fact_nat__neq__iff, fact_nat__1__eq__mult__iff, fact_nonzero__inverse__eq__divide, fact_offset__poly__eq__0__iff, fact_mult__left__less__imp__less, fact_diff__mult__distrib2, fact_dvd_Ole__less, arity_Nat__Onat__Groups_Ominus, fact_degree__pCons__eq, fact_sgn__poly__def, fact_smult__eq__0__iff, arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, fact_add__mult__distrib2, fact_eq__add__iff1, fact_Limits_Ominus__diff__minus, fact_less__not__refl3, arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, fact_one__less__mult, fact_add__left__cancel, fact_poly__gcd__minus__left, fact_add__pCons, fact_neg__less__nonneg, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, arity_Complex__Ocomplex__RealVector_Oreal__normed__field, arity_Complex__Ocomplex__Rings_Ozero__neq__one, fact_sgn__sgn, fact_mod__Suc, fact_add__right__cancel, fact_mult__strict__mono_H, fact_poly__pCons, fact_nat__diff__split__asm, fact_nat__mult__dvd__cancel__disj, fact_dvd_Oorder__refl, fact_mult__nonneg__nonneg, fact_zero__less__mult__pos2, fact_dvd__mult, fact_frac__le, fact_poly__rec__pCons, fact_frac__eq__eq, fact_one__less__inverse, fact_nat__size, fact_degree__le, fact_dvd_Oord__le__eq__trans, arity_Complex__Ocomplex__Rings_Ocomm__semiring, fact_nat__add__left__cancel__le, fact_less__eq__poly__def, fact_double__zero__sym, fact_divide__pos__pos, fact_le__imp__inverse__le__neg, fact_neg__0__equal__iff__equal, fact_double__compl, fact_le__diff__conv, fact_pdivmod__rel__smult__left, arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, fact_divide__neg__neg, fact_right__minus, fact_mult__left__mono, fact_mult__left_Oadd, fact_mult__imp__less__div__pos, fact_add__divide__eq__iff, fact_mult__left_Ozero, fact_one__neq__zero, fact_left__minus, fact_diff__cancel, fact_divide__neg__pos, fact_le__add__iff1, fact_monom__eq__0__iff, fact_split__mod, fact_mult__dvd__mono, fact_poly__1, fact_less__Suc__eq__0__disj, fact_divide__nonneg__pos, fact_le__Suc__eq, fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, fact_dvd__smult__cancel, fact_less__add__iff2, arity_Polynomial__Opoly__Rings_Oring, fact_add__strict__mono, fact_diff__divide__eq__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_offset__poly__eq__0__lemma, fact_frac__less, arity_Polynomial__Opoly__Groups_Oab__group__add, fact_poly__pcompose, arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, arity_Nat__Onat__Groups_Ocomm__monoid__add, fact_nat__mult__le__cancel1, fact_le__add__diff__inverse2, fact_Suc__mult__less__cancel1, fact_add__num__frac, fact_degree__offset__poly, arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_equation__minus__iff, fact_inverse__eq__divide, fact_nat__diff__add__eq2, fact_poly__gcd__dvd1, fact_mult__neg__pos, arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, arity_Polynomial__Opoly__Groups_Oab__semigroup__add, fact_less__antisym, fact_not__one__le__zero, arity_Polynomial__Opoly__Rings_Olinordered__idom, fact_Suc__le__eq, fact_add__diff__cancel, arity_fun__Lattices_Oboolean__algebra, fact_mult__cancel2, arity_Polynomial__Opoly__Groups_Ouminus, fact_poly__minus, arity_Polynomial__Opoly__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Ocomm__semiring, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_mult__less__le__imp__less, fact_nat__mult__assoc, fact_equal__neg__zero, fact_smult__add__left, arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, fact_less__eq__Suc__le, fact_le__imp__inverse__le, fact_less__imp__diff__less, fact_mod__le__divisor, fact_inverse__eq__imp__eq, help_c__fequal__1, fact_sgn__0__0, fact_Suc__pred_H, fact_diff__add__cancel, arity_Complex__Ocomplex__Rings_Oring, fact_nat_Osize_I1_J, fact_pdivmod__rel__by__0__iff, fact_comm__mult__strict__left__mono, arity_Nat__Onat__Groups_Omonoid__add, fact_monom__0, fact_mult__monom, fact_not__sum__squares__lt__zero, fact_pos__poly__mult, fact_divide__eq__eq, fact_inverse__nonnegative__iff__nonnegative, fact_mult__nonneg__nonpos2, fact_less__add__Suc2, arity_Polynomial__Opoly__Groups_Omonoid__mult, fact_uminus__apply, fact_mult_Ominus__left, fact_pdivmod__rel__unique, fact_nat__mult__eq__cancel1, fact_pCons__eq__iff, fact_dvd_Oless__not__sym, fact_degree__add__less, fact_minus__minus, fact_dvd__mult__cancel1, fact_dvd__diffD1, fact_divide__nonpos__pos, fact_mod__diff__eq, fact_dvd__refl, fact_smult__0__left, fact_minus__add__distrib, fact_smult__monom, fact_diffs0__imp__equal, fact_diff__diff__left, fact_nonzero__divide__eq__eq, arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, fact_divide__less__0__iff, arity_Nat__Onat__Groups_Ozero, fact_pCons__eq__0__iff, arity_Complex__Ocomplex__Groups_Oone, fact_add__is__1, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, fact_less__minus__iff, fact_inverse__unique, fact_linorder__neqE__nat, fact_mult__less__mono2, arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, fact_dvd__diff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_nat__mult__less__cancel1, fact_coeff__pCons, fact_diff__Suc__diff__eq2, fact_dvd_Oneq__le__trans, fact_less__poly__def, arity_Nat__Onat__Groups_Ocomm__monoid__mult, fact_add__nonpos__nonpos, fact_diff__add__assoc2, fact_mult_Ozero__right, fact_inverse__nonzero__iff__nonzero, fact_mod__geq, fact_sgn__times, fact_frac__less2, fact_dvd__add, arity_Complex__Ocomplex__Rings_Oring__1, fact_diff__diff__right, fact_one__poly__def, fact_mod__minus__eq, fact_order__root, arity_Complex__Ocomplex__Groups_Ouminus, arity_Complex__Ocomplex__Rings_Odivision__ring, fact_add__nonneg__pos, fact_mult__less__cancel__right__disj, fact_Suc__mult__cancel1, fact_mult__strict__right__mono, fact_mult__poly__add__left, fact_Suc__le__lessD, fact_add__increasing, fact_not__add__less1, fact_expand__poly__eq, fact_mult__right_Oadd, fact_nat__le__add__iff2, fact_ext, arity_Nat__Onat__Rings_Olinordered__semiring, fact_poly__gcd_Oleft__commute, fact_eq__diff__iff, fact_mult_Oadd__left, fact_degree__add__le, arity_Complex__Ocomplex__Rings_Ocomm__ring__1, fact_nat__lt__two__imp__zero__or__one, fact_times__divide__eq__right, fact_Suc__neq__Zero, fact_divide__le__0__iff, arity_Polynomial__Opoly__Rings_Omult__zero, fact_inverse__eq__1__iff, fact_le__divide__eq, arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors, fact_Suc__inject, fact_dvd__poly__gcd__iff, fact_minus__dvd__iff, fact_less__diff__conv, fact_divide__right__mono__neg, fact_diff__poly__code_I2_J, fact_crossproduct__noteq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_le__imp__neg__le, arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, fact_poly__gcd_Ocommute, fact_mult__le__cancel__left__pos, fact_less__add__iff1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_division__ring__inverse__diff, fact_zero__less__double__add__iff__zero__less__single__add, fact_poly__gcd__code, fact_eq__divide__imp, fact_add__eq__self__zero, fact_diff__less__Suc, fact_mod__poly__less, fact_divide_Ozero, fact_mult__le__cancel2, fact_dvd_Oless__imp__le, fact_mult__le__mono, fact_dvd__imp__le, fact_nat__mult__dvd__cancel1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_mult__zero__right, fact_nat__less__add__iff1, fact_divide__zero, fact_mult__le__0__iff, fact_divide__self__if, fact_mult__is__0, fact_nat__add__left__cancel, fact_Suc__diff__1, fact_n__not__Suc__n, fact_nat__le__linear, fact_le__iff__diff__le__0, fact_poly__rec__0, fact_mod__diff__left__eq, arity_Nat__Onat__Rings_Omult__zero, fact_inverse__positive__iff__positive, fact_inverse__mult__distrib, fact_less__minus__self__iff, fact_add__strict__left__mono, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_sum__squares__gt__zero__iff, fact_nat__0__less__mult__iff, fact_add__gr__0, arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, fact_add__diff__assoc2, fact_inverse__eq__iff__eq, fact_poly__gcd__1__right, fact_dvd__1__left, fact_diff__eq__diff__less, arity_Polynomial__Opoly__Rings_Ozero__neq__one, fact_add__mult__distrib, fact_le__add__diff, fact_pos__poly__total, arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, fact_inverse__nonpositive__iff__nonpositive, fact_diff__poly__code_I1_J, fact_add__Suc, fact_diff__add__assoc, fact_nat__le__add__iff1, fact_mult__less__cancel1, fact_dvd__triv__left, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_diff__divide__distrib, fact_coeff__mult__degree__sum, fact_mult__divide__mult__cancel__right, fact_nat_Osize_I2_J, fact_minus__unique, fact_poly__power, fact_diff__less__mono2, fact_dvd_Oless__imp__not__eq, fact_divide__zero__left, arity_Nat__Onat__Rings_Oordered__cancel__semiring, fact_diff__mult__distrib, fact_dvd__diff__nat, fact_le__Suc__ex__iff, arity_Nat__Onat__Rings_Odvd, fact_degree__synthetic__div, fact_Suc__eq__plus1__left, fact_field__le__mult__one__interval, arity_Complex__Ocomplex__Rings_Ono__zero__divisors, fact_zero__less__one, fact_add_Ocomm__neutral, fact_Zero__not__Suc, fact_dvd__mult__right, arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, fact_one__le__inverse, fact_left__inverse, fact_mult__strict__mono, fact_diff__less__mono, fact_Suc__leD, fact_neg__equal__zero, fact_nonzero__inverse__minus__eq, fact_add__minus__cancel, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_zero__less__divide__iff, fact_psize__def, fact_nonzero__imp__inverse__nonzero, fact_pos__divide__less__eq, arity_Nat__Onat__Rings_Oordered__semiring, fact_mult__Suc, fact_less__trans__Suc, fact_le__minus__self__iff, fact_mod__mult__self3, fact_diff__frac__eq, fact_eq__add__iff2, fact_poly__rec_Osimps, arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, fact_mult__right__le__one__le, fact_sgn__1__neg, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_mult__zero__left, fact_left__add__mult__distrib, fact_add__scale__eq__noteq, fact_Nat_Odiff__diff__eq, fact_le__refl, fact_nat__add__assoc, fact_mult__imp__div__pos__le, fact_less__not__refl2, fact_field__class_Onormalizing__field__rules_I2_J, fact_poly__gcd__zero__iff, fact_inverse__le__imp__le__neg, fact_le__add1, fact_mult__cancel1, fact_trans__le__add2, fact_monom__eq__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_less__add__Suc1, fact_nat__case__Suc, fact_One__nat__def, fact_mult__diff__mult, fact_mod__eq__0__iff, fact_divide_Oadd, fact_le__imp__less__Suc, fact_mod__less__eq__dividend, fact_sgn__zero__iff, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, fact_coeff__smult, fact_nonzero__minus__divide__divide, fact_smult__0__right, fact_leading__coeff__0__iff, fact_Suc__mult__le__cancel1, fact_ab__left__minus, fact_sgn0, fact_add__neg__neg, arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, fact_minus__diff__eq, fact_less__imp__inverse__less__neg, fact_comm__semiring__class_Odistrib, fact_square__eq__iff, fact_smult__dvd__iff, fact_nonzero__minus__divide__right, fact_add__is__0, fact_nat__diff__add__eq1, fact_termination__basic__simps_I3_J, fact_divide__diff__eq__iff, fact_times__divide__times__eq, fact_sgn__pos, fact_inverse__less__imp__less__neg, fact_ab__diff__minus, fact_Deriv_Oadd__diff__add, fact_mult__right__mono, fact_pCons__def, fact_diff__minus__eq__add, fact_inverse__le__imp__le, fact_mult__le__mono1, fact_diff__self__eq__0, fact_add__eq__0__iff, fact_minus__poly__code_I2_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_diff__add__0, fact_dvd__minus__iff, fact_add__pos__pos, fact_nat__case__0, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, fact_add__0, fact_poly__mod__minus__right, arity_Polynomial__Opoly__Rings_Oordered__ring, fact_nat__less__add__iff2, fact_add__nonneg__nonneg, fact_nat__eq__add__iff1, fact_less__imp__add__positive, fact_Suc__eq__plus1, fact_dvd__mult__cancel, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, fact_neg__equal__iff__equal, fact_degree__power__le, fact_sgn__greater, fact_inverse__minus__eq, fact_degree__minus, fact_compl__eq__compl__iff, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, fact_pos__poly__add, fact_coeff__pCons__Suc, fact_smult__dvd, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, fact_mult__nonpos__nonneg, fact_Suc__diff__le, fact_pos__poly__pCons, arity_Polynomial__Opoly__Rings_Osemiring, fact_Zero__neq__Suc, fact_poly__gcd__0__0, fact_degree__add__eq__left, arity_Nat__Onat__Groups_Oab__semigroup__add, arity_Nat__Onat__Rings_Olinordered__semidom, arity_Complex__Ocomplex__Groups_Omonoid__mult, fact_add__left__mono, fact_synthetic__div__eq__0__iff, fact_Suc__pred, fact_nat__dvd__1__iff__1, fact_divide__less__eq, fact_le__mod__geq, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_mult__right_Ominus, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_poly__gcd__unique, fact_sgn__if, fact_less__1__mult, fact_right__inverse, fact_compl__le__compl__iff, fact_le0, fact_coeff__monom, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_poly__diff, fact_mod__smult__left, fact_le__diff__conv2, fact_mult__pos__pos, fact_minus__mult__minus, fact_ex__least__nat__less, fact_crossproduct__eq, fact_monom__eq__iff, fact_square__eq__1__iff, fact_dvd_Oantisym, fact_neg__less__divide__eq, fact_le__trans, fact_diff__Suc__diff__eq1, fact_comm__mult__left__mono, fact_degree__mod__less, fact_inf__period_I3_J, arity_fun__Groups_Ominus, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_dvd_Ole__neq__trans, fact_add__less__le__mono, fact_dvd__antisym, arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, fact_less__add__one, fact_degree__monom__eq, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_mult__less__imp__less__right, fact_less__Suc__eq, fact_diff__eq__diff__less__eq, fact_divide__strict__left__mono, fact_add__leE, fact_dvd__smult__iff, fact_right__minus__eq, fact_neg__0__le__iff__le, fact_diff__Suc__1, fact_poly__gcd_Osimps_I1_J, fact_zero__neq__one, fact_nat__add__commute, fact_mult__smult__left, fact_synthetic__div__unique, fact_add__poly__code_I1_J, fact_degree__diff__less, fact_Suc__less__eq, fact_mult__neg__neg, fact_poly__gcd__1__left, fact_mult_Odiff__left, fact_coeff__0, arity_Polynomial__Opoly__Groups_Ogroup__add, fact_sgn__one, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, fact_degree__mult__le, fact_zero__less__Suc, fact_mod__poly__eq, fact_eq__zero__or__degree__less, fact_plus__nat_Oadd__0, arity_Complex__Ocomplex__Rings_Ocomm__ring, fact_less__divide__eq, fact_mult_Ocomm__neutral, fact_dvd_Oless__le, fact_add__nonpos__neg, fact_le__SucE, fact_dvd_Oless__le__trans, fact_divide_Odiff, fact_nat__mult__commute, arity_Polynomial__Opoly__Divides_Oring__div, fact_mod__Suc__eq__Suc__mod, arity_Polynomial__Opoly__Rings_Olinordered__semiring, fact_eq__imp__le, fact_diff__add__inverse2, arity_Complex__Ocomplex__Int_Oring__char__0, fact_neg__divide__less__eq, fact_diff__eq__diff__eq, fact_minus__le__self__iff, fact_nat_Osize_I3_J, fact_add__strict__increasing, fact_le__less__Suc__eq, fact_not__pos__poly__0, arity_Polynomial__Opoly__Rings_Ocomm__ring__1, fact_neq0__conv, fact_Suc__n__not__n, fact_mult__left__mono__neg, fact_synthetic__div__unique__lemma, fact_le__antisym, fact_add__divide__distrib, fact_diff__le__mono, arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, arity_Complex__Ocomplex__Rings_Omult__zero, fact_mult__Suc__right, fact_add__frac__num, fact_minus__equation__iff, fact_divide__strict__right__mono, fact_mult__0__right, fact_mult__less__cancel__left__pos, fact_trans__le__add1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_degree__monom__le, fact_zero__less__mult__pos, arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Ocomm__semiring, arity_Polynomial__Opoly__Rings_Ono__zero__divisors, fact_double__eq__0__iff, fact_le__0__eq, fact_dvd__0__left, fact_pcompose__pCons, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_mult__less__cancel2, fact_dvd__1__iff__1, fact_mod__lemma, fact_mult__1__right, fact_zero__less__two, fact_diff__is__0__eq, arity_Polynomial__Opoly__Groups_Ozero, fact_pdivmod__rel__unique__mod, fact_dvd__iff__poly__eq__0, fact_add__le__mono, fact_divide__nonneg__neg, arity_Nat__Onat__Rings_Osemiring, fact_termination__basic__simps_I1_J, fact_less__iff__Suc__add, fact_sum__squares__eq__zero__iff, fact_le__add__diff__inverse, fact_less__Suc0, fact_pos__poly__def, fact_dvd_Ole__less__trans, fact_diff__monom, fact_add__diff__inverse, fact_convex__bound__le, fact_nat__mult__eq__cancel__disj, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_mult__less__imp__less__left, fact_le__diff__iff, fact_smult__minus__right, arity_Nat__Onat__Groups_Oone, fact_add__imp__eq, fact_le__square, fact_add__less__mono1, arity_Polynomial__Opoly__Rings_Olinordered__ring, arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, fact_DERIV__mult__lemma, fact_ab__semigroup__add__class_Oadd__ac_I1_J, fact_diff__Suc__Suc, fact_dvd__mult__left, fact_coeff__inject, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_degree__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_mod__minus__cong, fact_dvd_Ole__imp__less__or__eq, fact_minus__poly__code_I1_J, fact_nat__less__le, arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, fact_no__zero__divisors, fact_sgn__1__pos, fact_less__iff__diff__less__0, fact_mult__eq__if, fact_Deriv_Oinverse__diff__inverse, fact_less__SucE, fact_gt__half__sum, fact_le__cube, fact_eq__divide__eq, fact_divisors__zero, fact_smult__diff__left, arity_Polynomial__Opoly__Groups_Oone, fact_poly__eq__iff, fact_degree__mult__eq, fact_inverse__negative__imp__negative, fact_field__inverse__zero, fact_nonzero__eq__divide__eq, fact_double__add__less__zero__iff__single__add__less__zero, fact_minus__divide__left, fact_one__le__inverse__iff, fact_less__diff__iff, fact_pdivmod__rel__0, fact_dvd_Oless__imp__not__eq2, fact_pdivmod__rel__pCons, fact_field__inverse, fact_less__half__sum, fact_add__Suc__shift, fact_dvd__mult__cancel__right, fact_pdivmod__rel__def, fact_divide__self, fact_coeff__diff, fact_less__SucI, fact_Suc__not__Zero, arity_Complex__Ocomplex__Groups_Ozero, fact_poly__gcd_Osimps_I2_J, arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, fact_mult__pCons__left, arity_Complex__Ocomplex__Groups_Ominus, fact_mult__1, arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, fact_mult_Odiff__right, fact_mod__mult__distrib, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 298.78/60.76 % No. of inferences in proof: 2211
% 298.78/60.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 60204 ms resp. 59602 ms w/o parsing
% 299.81/61.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 299.88/61.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------