TSTP Solution File: SWW255+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SWW255+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 : Tue May 7 08:23:26 EDT 2024
% Result : Theorem 99.59s 23.54s
% Output : Refutation 100.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1314
% Syntax : Number of formulae : 2512 ( 692 unt; 118 typ; 0 def)
% Number of atoms : 6202 (1663 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 32509 ( 377 ~; 147 |; 508 &;28324 @)
% ( 231 <=>;2922 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 155 ( 155 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 118 usr; 13 con; 0-5 aty)
% Number of variables : 5151 ( 0 ^5043 !; 108 ?;5151 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: $i > $i > $i > $i ).
thf(c_Rings_Oinverse__class_Oinverse_type,type,
c_Rings_Oinverse__class_Oinverse: $i > $i > $i ).
thf(v_q_____type,type,
v_q____: $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(v_w_____type,type,
v_w____: $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(v_k_____type,type,
v_k____: $i ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(class_Groups_Ouminus_type,type,
class_Groups_Ouminus: $i > $o ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
thf(class_Rings_Oordered__semiring_type,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(c_Rings_Odvd__class_Odvd_type,type,
c_Rings_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(c_Transcendental_Oln_type,type,
c_Transcendental_Oln: $i > $i ).
thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(c_RComplete_Onatfloor_type,type,
c_RComplete_Onatfloor: $i > $i ).
thf(c_RealDef_Oreal_type,type,
c_RealDef_Oreal: $i > $i > $i ).
thf(class_Rings_Oordered__cancel__semiring_type,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Rings_Ocomm__semiring_type,type,
class_Rings_Ocomm__semiring: $i > $o ).
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_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_fequal_type,type,
c_fequal: $i > $i > $i ).
thf(class_Groups_Ogroup__add_type,type,
class_Groups_Ogroup__add: $i > $o ).
thf(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(class_Rings_Osemiring_type,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
thf(c_RComplete_Onatceiling_type,type,
c_RComplete_Onatceiling: $i > $i ).
thf(class_Groups_Oordered__ab__semigroup__add_type,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_type,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(class_Rings_Oordered__ring_type,type,
class_Rings_Oordered__ring: $i > $o ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(class_Rings_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Rings_Ocomm__ring_type,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_type,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Rings_Odvd_type,type,
class_Rings_Odvd: $i > $o ).
thf(class_Rings_Olinordered__semiring__1__strict_type,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_SEQ_OBseq_type,type,
c_SEQ_OBseq: $i > $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_type,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(c_Polynomial_Osynthetic__div_type,type,
c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_type,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(c_Polynomial_Omonom_type,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(class_Groups_Ocancel__comm__monoid__add_type,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Fields_Ofield__inverse__zero_type,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_type,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Osemiring__0_type,type,
class_Rings_Osemiring__0: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(class_Rings_Olinordered__semiring_type,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_type,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $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_Fields_Olinordered__field__inverse__zero_type,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
thf(c_Polynomial_Opos__poly_type,type,
c_Polynomial_Opos__poly: $i > $i > $o ).
thf(c_Polynomial_Opcompose_type,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_RealVector_Oreal__normed__div__algebra_type,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: $i > $i > $i > $o ).
thf(c_Power_Opower_Opower_type,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(c_Complex_Orcis_type,type,
c_Complex_Orcis: $i > $i > $i ).
thf(v_pa_____type,type,
v_pa____: $i ).
thf(v_c_____type,type,
v_c____: $i ).
thf(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(v_s_____type,type,
v_s____: $i ).
thf(c_Complex_Ocis_type,type,
c_Complex_Ocis: $i > $i ).
thf(c_Complex_Oexpi_type,type,
c_Complex_Oexpi: $i > $i ).
thf(v_p_type,type,
v_p: $i ).
thf(class_Lattices_Oab__semigroup__idem__mult_type,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Polynomial_Opoly__rec_type,type,
c_Polynomial_Opoly__rec: $i > $i > $i > $i > $i > $i ).
thf(c_SEQ_Oincseq_type,type,
c_SEQ_Oincseq: $i > $i > $o ).
thf(c_If_type,type,
c_If: $i > $i > $i > $i > $i ).
thf(c_SEQ_Odecseq_type,type,
c_SEQ_Odecseq: $i > $i > $o ).
thf(349,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
thf(2163,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)],[349]) ).
thf(522,axiom,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
thf(2630,plain,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(1369,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
thf(1633,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)],[159]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
thf(3167,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[687]) ).
thf(757,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(3397,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(3449,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[774]) ).
thf(416,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(2331,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)],[416]) ).
thf(271,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
thf(1956,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(366,axiom,
( ( c_RComplete_Onatfloor @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__one) ).
thf(2199,plain,
( ( c_RComplete_Onatfloor @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(1665,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)],[172]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
<=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff) ).
thf(1501,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) )
=> ( c_SEQ_OBseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
thf(4201,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ B ) )
& ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(460,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
thf(2452,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)],[460]) ).
thf(1112,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(4560,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(250,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
thf(1879,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(1337,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)],[50]) ).
thf(186,axiom,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(1718,plain,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(2094,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(930,axiom,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_a00) ).
thf(3944,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(512,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
thf(2612,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(977,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
thf(4094,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)],[977]) ).
thf(107,axiom,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(1469,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(2295,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)],[403]) ).
thf(406,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/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(2306,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)],[406]) ).
thf(742,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/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(3345,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)],[742]) ).
thf(418,axiom,
class_Rings_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(2336,plain,
class_Rings_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(339,axiom,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
thf(2131,plain,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(319,axiom,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
thf(2072,plain,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(849,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).
thf(3661,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Nat_OSuc @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth2) ).
thf(4062,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Nat_OSuc @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(287,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(1995,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)],[287]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(2263,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(891,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/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
thf(3798,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)],[891]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
thf(1559,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)],[132]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(2876,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(19,axiom,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
thf(1237,plain,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1000,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(4183,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)],[1000]) ).
thf(619,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 ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(2921,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 ) @ ( hAPP @ ( hAPP @ ( 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)],[619]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(3698,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
thf(1315,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)],[45]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(2787,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[576]) ).
thf(478,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/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(2499,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)],[478]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(1982,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(453,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(2427,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)],[453]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(2480,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)],[470]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(1750,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)],[202]) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__0) ).
thf(2210,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)],[371]) ).
thf(334,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
thf(2117,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)],[334]) ).
thf(1049,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(4339,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(4075,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(518,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6a) ).
thf(2622,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(314,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(2062,plain,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(3040,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(673,axiom,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096) ).
thf(3108,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
thf(1305,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(856,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(3680,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)],[856]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
thf(1200,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)],[3]) ).
thf(805,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/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
thf(3534,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)],[805]) ).
thf(1161,axiom,
? [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ ) )
& ! [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_c____ @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096) ).
thf(4714,plain,
? [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ ) )
& ! [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_c____ @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(638,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(2976,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(707,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(3230,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(896,axiom,
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_s____ ) @ v_k____ ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I3_J) ).
thf(3813,plain,
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_s____ ) @ v_k____ ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(476,axiom,
class_Rings_Oring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
thf(2495,plain,
class_Rings_Oring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(1808,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(533,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/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(2659,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)],[533]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(3509,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring__1 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ ( c_Polynomial_Omonom @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__replicate__append) ).
thf(3285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring__1 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ ( c_Polynomial_Omonom @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(632,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/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(2953,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)],[632]) ).
thf(76,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(1401,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(1422,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)],[85]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
thf(2947,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[630]) ).
thf(328,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/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(2099,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)],[328]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).
thf(2282,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
thf(1591,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)],[143]) ).
thf(791,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/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
thf(3498,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)],[791]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(2380,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)],[437]) ).
thf(278,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
thf(1971,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)],[278]) ).
thf(1133,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(4614,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(1170,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(4747,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1090,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).
thf(4487,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[1090]) ).
thf(1020,axiom,
class_Groups_Ouminus @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
thf(4234,plain,
class_Groups_Ouminus @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(168,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
thf(1655,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)],[168]) ).
thf(1169,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(4739,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(193,axiom,
( ( c_RComplete_Onatceiling @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__one) ).
thf(1735,plain,
( ( c_RComplete_Onatceiling @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(2316,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)],[409]) ).
thf(247,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
thf(1872,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)],[247]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(3616,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(3781,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[887]) ).
thf(1115,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(4564,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)],[1115]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Transcendental_Oln @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__realpow) ).
thf(2901,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Transcendental_Oln @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).
thf(2844,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(102,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
thf(1458,plain,
class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(722,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(3276,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)],[722]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
thf(1497,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)],[114]) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(1705,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)],[181]) ).
thf(1110,axiom,
class_Groups_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
thf(4543,plain,
class_Groups_Ozero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(1138,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/sandbox2/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
thf(4633,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)],[1138]) ).
thf(1065,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(4403,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[1065]) ).
thf(770,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(3439,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)],[770]) ).
thf(510,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/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(2607,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)],[510]) ).
thf(543,axiom,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(2686,plain,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(1119,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/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(4575,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)],[1119]) ).
thf(43,axiom,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(1310,plain,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(3332,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(751,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(3367,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(842,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(3648,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)],[842]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
thf(3365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( 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)],[750]) ).
thf(618,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
thf(2918,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( c_Polynomial_Osmult @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(981,axiom,
! [A: $i] :
( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( c_Complex_Ocis @ A ) )
= ( c_Complex_Ocis @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__inverse) ).
thf(4110,plain,
! [A: $i] :
( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( c_Complex_Ocis @ A ) )
= ( c_Complex_Ocis @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(243,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
thf(1867,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(4220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[1015]) ).
thf(358,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
thf(2184,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)],[358]) ).
thf(520,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
thf(2627,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(352,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
thf(2168,plain,
class_Int_Oring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
<=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).
thf(1919,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(462,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/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
thf(2459,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)],[462]) ).
thf(760,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(3414,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)],[760]) ).
thf(52,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
thf(1342,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)],[52]) ).
thf(1033,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(4294,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(815,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
thf(3562,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)],[815]) ).
thf(162,axiom,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1640,plain,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(1075,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
thf(4435,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(306,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(2042,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(56,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
thf(1354,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
thf(2146,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)],[345]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(1222,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)],[13]) ).
thf(428,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
thf(2360,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)],[428]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).
thf(1746,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)],[200]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(3236,plain,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( 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)],[710]) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(2432,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)],[455]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(3249,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
= A ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
= A )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
thf(4679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( 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)],[1149]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(3088,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( 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)],[669]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).
thf(1359,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1007,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/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
thf(4198,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)],[1007]) ).
thf(1179,axiom,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
thf(4775,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1059,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
thf(4386,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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(3335,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
thf(4047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(744,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(3350,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(808,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__zero__iff) ).
thf(3545,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(555,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ C ) ) @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean4) ).
thf(2723,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ C ) ) @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(4142,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).
thf(2046,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)],[309]) ).
thf(474,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/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
thf(2491,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)],[474]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
<=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).
thf(2548,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
thf(3947,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1189,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__zero) ).
thf(4803,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(1601,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)],[146]) ).
thf(778,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).
thf(3466,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(957,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/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
thf(4030,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)],[957]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(4137,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(4607,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(60,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
thf(1366,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)],[60]) ).
thf(317,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/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(2067,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)],[317]) ).
thf(276,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(1967,plain,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1041,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/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(4322,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)],[1041]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(3880,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(120,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
thf(1518,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1132,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/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).
thf(4610,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)],[1132]) ).
thf(486,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(2531,plain,
class_Rings_Osemiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(445,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
thf(2405,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)],[445]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(1228,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)],[15]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(1623,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(928,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).
thf(3938,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[928]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
thf(1792,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)],[212]) ).
thf(305,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/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
thf(2039,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)],[305]) ).
thf(536,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/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(2667,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)],[536]) ).
thf(790,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(3495,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)],[790]) ).
thf(1174,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/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(4761,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)],[1174]) ).
thf(551,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
thf(2708,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)],[551]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_Omonom @ D @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
thf(3653,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_Omonom @ D @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1181,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/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
thf(4778,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)],[1181]) ).
thf(542,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(2682,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)],[542]) ).
thf(807,axiom,
! [A: $i,B: $i] :
( ( c_Complex_Oexpi @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Oexpi @ B ) ) @ ( c_Complex_Oexpi @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expi__add) ).
thf(3542,plain,
! [A: $i,B: $i] :
( ( c_Complex_Oexpi @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Oexpi @ B ) ) @ ( c_Complex_Oexpi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1455,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)],[100]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(3442,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(718,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(3263,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1077,axiom,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ v_c____ )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pc0) ).
thf(4439,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ v_c____ )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(3976,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(414,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
thf(2328,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)],[414]) ).
thf(1102,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ononneg__bounded) ).
thf(4524,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(2735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(1114,axiom,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
thf(4563,plain,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(548,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(2698,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(39,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1298,plain,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(2339,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(858,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/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
thf(3689,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)],[858]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(3342,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[741]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
<=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff1a) ).
thf(2269,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) )
=> ( c_SEQ_OBseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(395,axiom,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(2274,plain,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(786,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ D ) @ B ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).
thf(3485,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 @ ( hAPP @ ( hAPP @ ( 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)],[786]) ).
thf(498,axiom,
! [A: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
thf(2562,plain,
! [A: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(472,axiom,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(2488,plain,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(892,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(3803,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)],[892]) ).
thf(337,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/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2126,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)],[337]) ).
thf(658,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(3043,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(908,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(3855,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(501,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/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
thf(2571,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)],[501]) ).
thf(866,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/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(3713,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)],[866]) ).
thf(546,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(2691,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)],[546]) ).
thf(353,axiom,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(2169,plain,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(1134,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
<=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ? [D: $i] :
! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( hAPP @ A @ E ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( hAPP @ A @ D ) ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff3) ).
thf(4617,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ? [D: $i] :
! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( hAPP @ A @ E ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( hAPP @ A @ D ) ) ) ) @ C ) ) )
& ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ? [D: $i] :
! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( hAPP @ A @ E ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( hAPP @ A @ D ) ) ) ) @ C ) )
=> ( c_SEQ_OBseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(4194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(149,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
thf(1609,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1029,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/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__0) ).
thf(4270,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)],[1029]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
thf(1641,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(3231,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(3099,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(1800,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)],[215]) ).
thf(984,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).
thf(4119,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)],[984]) ).
thf(799,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
thf(3517,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(3840,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(68,axiom,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(1379,plain,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1052,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(4353,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)],[1052]) ).
thf(1183,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/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(4788,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)],[1183]) ).
thf(433,axiom,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
thf(2373,plain,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(1135,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/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(4622,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)],[1135]) ).
thf(525,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2635,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(623,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/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(2929,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)],[623]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
thf(3312,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(846,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/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(3657,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)],[846]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(1931,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)],[265]) ).
thf(875,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(3734,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
thf(2520,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(558,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
thf(2730,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(404,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/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
thf(2301,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)],[404]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).
thf(1815,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)],[222]) ).
thf(112,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
thf(1494,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)],[112]) ).
thf(641,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero__iff) ).
thf(2989,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(1362,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).
thf(4793,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(813,axiom,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
thf(3557,plain,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(210,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
thf(1778,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)],[210]) ).
thf(440,axiom,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(2388,plain,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(911,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(3866,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(488,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(2533,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)],[488]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
thf(1232,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)],[17]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(3268,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(293,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/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(2007,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)],[293]) ).
thf(375,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
thf(2222,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)],[375]) ).
thf(1120,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(4578,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(953,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
thf(4018,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(871,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
thf(3724,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(574,axiom,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rnc) ).
thf(2782,plain,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(2893,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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)],[611]) ).
thf(781,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/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
thf(3473,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)],[781]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( B
= ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__power) ).
thf(1864,plain,
! [A: $i,B: $i] :
( ( B
= ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1164,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(4724,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[1164]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
=> ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).
thf(1828,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
=> ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(2540,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1152,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(4686,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(572,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/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
thf(2777,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)],[572]) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
thf(2073,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)],[320]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
thf(2950,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[631]) ).
thf(379,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(2237,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)],[379]) ).
thf(514,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(2616,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(1062,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/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(4396,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)],[1062]) ).
thf(105,axiom,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(1465,plain,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(4329,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(937,axiom,
( ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).
thf(3966,plain,
( ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(184,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
thf(1714,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(3670,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(1167,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
thf(4733,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(2291,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
thf(1383,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)],[70]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(4134,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(747,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/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
thf(3357,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)],[747]) ).
thf(496,axiom,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(2555,plain,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(730,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 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
thf(3300,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 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(944,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(3986,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(66,axiom,
class_Groups_Ozero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(1377,plain,
class_Groups_Ozero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(1215,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)],[9]) ).
thf(96,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
thf(1447,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)],[96]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
thf(3505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(1433,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)],[90]) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
thf(1405,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)],[78]) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
thf(1943,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)],[267]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(4082,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[975]) ).
thf(754,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/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
thf(3389,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)],[754]) ).
thf(479,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
thf(2508,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)],[479]) ).
thf(806,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 ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_order) ).
thf(3537,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 ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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)],[806]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
thf(1928,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)],[264]) ).
thf(516,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2618,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)],[516]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
thf(2833,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(876,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(3739,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)],[876]) ).
thf(362,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(2190,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(3421,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ C ) )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
thf(4364,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( 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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(452,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/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
thf(2424,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)],[452]) ).
thf(432,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
thf(2371,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(639,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(2979,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1036,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/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
thf(4307,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)],[1036]) ).
thf(342,axiom,
class_Rings_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(2137,plain,
class_Rings_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(961,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).
thf(4040,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)],[961]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(3756,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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)],[883]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
thf(3955,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(579,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ C @ B ) ) @ A )
= ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DeMoivre2) ).
thf(2799,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ C @ B ) ) @ A )
= ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(960,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(4038,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(528,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/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(2639,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)],[528]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(2965,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(1100,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(4519,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(145,axiom,
class_Groups_Oone @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(1600,plain,
class_Groups_Oone @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1160,axiom,
! [A: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
thf(4707,plain,
! [A: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(913,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 ) ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(3870,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 ) ) @ ( hAPP @ ( hAPP @ ( 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 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(3588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[822]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(4379,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(178,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(1697,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
thf(1242,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)],[22]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power) ).
thf(3559,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(4588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(3906,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(1521,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)],[122]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(3492,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(553,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/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
thf(2718,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)],[553]) ).
thf(368,axiom,
class_Groups_Oone @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(2205,plain,
class_Groups_Oone @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1086,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(4475,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(2982,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odvd @ D )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
thf(2884,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odvd @ D )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(768,axiom,
class_Fields_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
thf(3435,plain,
class_Fields_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1157,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(4700,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[1157]) ).
thf(671,axiom,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_q____ )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q_I1_J) ).
thf(3097,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_q____ )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1130,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(4604,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(3857,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(793,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(3503,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(1013,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/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(4216,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)],[1013]) ).
thf(731,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__eq__zero__iff) ).
thf(3303,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
thf(1691,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)],[177]) ).
thf(92,axiom,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
thf(1438,plain,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(907,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(3852,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[907]) ).
thf(837,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(3635,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(3186,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(735,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(3318,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
thf(1470,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)],[108]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( c_fequal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( c_fequal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(3037,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
thf(1604,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)],[147]) ).
thf(918,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(3899,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(943,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(3984,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(3265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(529,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/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
thf(2646,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)],[529]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
thf(1783,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(562,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(2737,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)],[562]) ).
thf(477,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/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
thf(2496,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)],[477]) ).
thf(577,axiom,
! [A: $i] :
( ( class_Power_Opower @ A )
=> ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Otimes__class_Otimes @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
thf(2790,plain,
! [A: $i] :
( ( class_Power_Opower @ A )
=> ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Otimes__class_Otimes @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(967,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(4059,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(244,axiom,
class_Rings_Odvd @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
thf(1868,plain,
class_Rings_Odvd @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(438,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/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
thf(2382,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)],[438]) ).
thf(810,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Obounded) ).
thf(3550,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(290,axiom,
class_Orderings_Oorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
thf(2000,plain,
class_Orderings_Oorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(1636,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)],[160]) ).
thf(550,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/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
thf(2705,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)],[550]) ).
thf(1083,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ononneg__bounded) ).
thf(4466,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(508,axiom,
class_Rings_Oidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
thf(2601,plain,
class_Rings_Oidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(383,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/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(2249,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)],[383]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
thf(2596,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Oincseq @ B @ A )
<=> ! [C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incseq__def) ).
thf(4375,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_SEQ_Oincseq @ B @ A )
=> ! [C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) @ ( hAPP @ A @ D ) ) ) )
& ( ! [C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) @ ( hAPP @ A @ D ) ) )
=> ( c_SEQ_Oincseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(828,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(3610,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(626,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(2937,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(4499,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(1092,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
thf(4493,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(340,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(2132,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)],[340]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ C ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
thf(3664,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ C ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(20,axiom,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
thf(1238,plain,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(780,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ v_c____ ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_c) ).
thf(3471,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ v_c____ ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
thf(1387,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)],[71]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
thf(1900,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)],[256]) ).
thf(952,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(4016,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)],[952]) ).
thf(581,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__add__one__self__le__self) ).
thf(2805,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(877,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
thf(3742,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(976,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/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(4091,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)],[976]) ).
thf(945,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).
thf(3989,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)],[945]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(4128,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(711,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cq0) ).
thf(3239,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( A != B )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(1824,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( A != B )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(346,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/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(2150,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)],[346]) ).
thf(702,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/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(3207,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)],[702]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
thf(3682,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
thf(4021,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( 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)],[954]) ).
thf(724,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
thf(3282,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1837,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)],[230]) ).
thf(991,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(4140,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(729,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/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
thf(3297,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)],[729]) ).
thf(819,axiom,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
thf(3578,plain,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(1951,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)],[269]) ).
thf(1043,axiom,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
thf(4327,plain,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
thf(2609,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1002,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(4187,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)],[1002]) ).
thf(229,axiom,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(1836,plain,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(1210,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)],[6]) ).
thf(372,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/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(2213,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)],[372]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).
thf(2313,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)],[408]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(1281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
thf(1573,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) )
& ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(531,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/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2653,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)],[531]) ).
thf(935,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/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
thf(3958,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)],[935]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(2445,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(696,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/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
thf(3191,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)],[696]) ).
thf(464,axiom,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(2464,plain,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).
thf(2873,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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)],[603]) ).
thf(59,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(1365,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(537,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/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(2670,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)],[537]) ).
thf(895,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).
thf(3810,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1122,axiom,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(4585,plain,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(468,axiom,
class_Rings_Osemiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(2477,plain,
class_Rings_Osemiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
thf(1968,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)],[277]) ).
thf(499,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Transcendental_Oln @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__inverse) ).
thf(2565,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Transcendental_Oln @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(37,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(1296,plain,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(869,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/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
thf(3718,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)],[869]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
thf(4776,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
thf(1687,plain,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(101,axiom,
class_Rings_Odvd @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).
thf(1457,plain,
class_Rings_Odvd @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
thf(2345,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)],[422]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
thf(3926,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(1392,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)],[74]) ).
thf(851,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
& ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ononneg__bounded) ).
thf(3667,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
& ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
thf(2228,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(330,axiom,
class_Rings_Oordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(2112,plain,
class_Rings_Oordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1291,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)],[36]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(3931,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(654,axiom,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ v_w____ )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ v_k____ ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_a____ @ v_s____ ) ) @ v_w____ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096poly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_A_061poly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Aw_A_094_Ak_A_K_Apoly_A_IpCons_Aa_As_J_Aw_096) ).
thf(3033,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ v_w____ )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ v_k____ ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_a____ @ v_s____ ) ) @ v_w____ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
<=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
thf(3408,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(1740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
thf(3445,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(956,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 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).
thf(4027,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 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( 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)],[956]) ).
thf(1039,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(4316,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)],[1039]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(1270,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)],[28]) ).
thf(436,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/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(2377,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)],[436]) ).
thf(217,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
thf(1804,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)],[217]) ).
thf(86,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
thf(1425,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(863,axiom,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
thf(3704,plain,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(800,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
thf(3518,plain,
class_Power_Opower @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(3746,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(843,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
thf(3650,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(527,axiom,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(2638,plain,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(392,axiom,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
thf(2268,plain,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(985,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
thf(4123,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(938,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(3968,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
thf(4808,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
thf(3831,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(332,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
thf(2115,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(784,axiom,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
thf(3482,plain,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(1762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(125,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero__iff) ).
thf(1534,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__cancel__iff) ).
thf(1953,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(4108,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1375,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)],[65]) ).
thf(1111,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/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(4544,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)],[1111]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).
thf(1856,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1139,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/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
thf(4636,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)],[1139]) ).
thf(141,axiom,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(1587,plain,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(249,axiom,
class_Groups_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(1878,plain,
class_Groups_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(3386,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(556,axiom,
class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
thf(2726,plain,
class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(2631,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(187,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
thf(1719,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(490,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
thf(2537,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(205,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
thf(1755,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( 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_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(929,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(3941,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(3060,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(690,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/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(3176,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)],[690]) ).
thf(1195,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(4817,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1148,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(4676,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(47,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1329,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).
thf(2023,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(905,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(3846,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
thf(4750,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(321,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/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(2080,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)],[321]) ).
thf(965,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(4054,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(304,axiom,
class_Power_Opower @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
thf(2038,plain,
class_Power_Opower @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).
thf(2085,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(818,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
thf(3573,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)],[818]) ).
thf(275,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/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(1964,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)],[275]) ).
thf(170,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
thf(1659,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)],[170]) ).
thf(645,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/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse) ).
thf(3000,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)],[645]) ).
thf(1121,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [C: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ C ) @ A ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).
thf(4582,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [C: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ C ) @ A ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
thf(4721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(196,axiom,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1739,plain,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
thf(1461,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(1072,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ! [B: $i] :
? [C: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean3) ).
thf(4425,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ! [B: $i] :
? [C: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(601,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/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
thf(2868,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)],[601]) ).
thf(825,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(3596,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(312,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/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
thf(2053,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)],[312]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(2240,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(232,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
thf(1842,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)],[232]) ).
thf(1066,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 ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).
thf(4406,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 ) @ ( hAPP @ ( hAPP @ ( 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)],[1066]) ).
thf(1004,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/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(4191,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)],[1004]) ).
thf(1098,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(4513,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(8,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1214,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(697,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(3194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(812,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(3555,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)],[812]) ).
thf(1082,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(4457,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
thf(1644,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)],[164]) ).
thf(1194,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/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
thf(4814,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)],[1194]) ).
thf(466,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
thf(2472,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)],[466]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(4180,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(728,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
& ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
thf(3294,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
& ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1168,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
thf(4736,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1104,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(4530,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(83,axiom,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(1419,plain,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(2968,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1249,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)],[25]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
<=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__def) ).
thf(4508,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) )
& ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
=> ( c_SEQ_OBseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(507,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/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
thf(2598,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)],[507]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
thf(3743,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(2581,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)],[503]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ D @ C ) ) @ ( c_Complex_Orcis @ B @ A ) )
= ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__mult) ).
thf(4540,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ D @ C ) ) @ ( c_Complex_Orcis @ B @ A ) )
= ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(833,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(3628,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(924,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
thf(3920,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(685,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(3162,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(1627,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)],[157]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1776,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)],[209]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
thf(1263,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)],[27]) ).
thf(845,axiom,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
thf(3656,plain,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(336,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(2125,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(1588,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)],[142]) ).
thf(489,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(2536,plain,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(38,axiom,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(1297,plain,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(3126,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(98,axiom,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1451,plain,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(405,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(2304,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)],[405]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(970,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(4068,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
thf(1831,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(425,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(2355,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)],[425]) ).
thf(1023,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(4244,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)],[1023]) ).
thf(1197,axiom,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
thf(4829,plain,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(899,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/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
thf(3819,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)],[899]) ).
thf(1022,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 ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(4237,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 ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1019,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).
thf(4231,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(236,axiom,
class_Groups_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(1852,plain,
class_Groups_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(88,axiom,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
thf(1429,plain,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(598,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2862,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(2766,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(859,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/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd) ).
thf(3692,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)],[859]) ).
thf(993,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/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(4152,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)],[993]) ).
thf(188,axiom,
class_Groups_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(1720,plain,
class_Groups_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(280,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/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
thf(1979,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)],[280]) ).
thf(647,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(3005,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(48,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean) ).
thf(1333,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(4535,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[1106]) ).
thf(621,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero) ).
thf(2926,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
thf(1202,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)],[4]) ).
thf(1175,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(4765,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
thf(3173,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[689]) ).
thf(564,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(2748,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(106,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(1466,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)],[106]) ).
thf(839,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(3639,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
thf(1515,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)],[119]) ).
thf(254,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
thf(1895,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(515,axiom,
class_Rings_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(2617,plain,
class_Rings_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ! [E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ B @ E ) ) @ A ) )
=> ( c_SEQ_OBseq @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BseqI2_H) ).
thf(2662,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ! [E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ B @ E ) ) @ A ) )
=> ( c_SEQ_OBseq @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(485,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(2529,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(3147,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(776,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/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
thf(3454,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)],[776]) ).
thf(524,axiom,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
thf(2634,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(920,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 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
thf(3903,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 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( 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)],[920]) ).
thf(285,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
thf(1991,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
thf(1318,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)],[46]) ).
thf(221,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(1814,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(704,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero__imp__gt__one) ).
thf(3225,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1116,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(4567,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ ( c_RComplete_Onatceiling @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).
thf(2208,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ ( c_RComplete_Onatceiling @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(974,axiom,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
thf(4081,plain,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(307,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
thf(2043,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)],[307]) ).
thf(723,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
thf(3279,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)],[723]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(3183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(1712,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
thf(1846,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)],[233]) ).
thf(948,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/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(3999,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)],[948]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
thf(1286,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(736,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(3321,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
thf(2368,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(447,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/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(2408,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)],[447]) ).
thf(578,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
thf(2793,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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(361,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(2189,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(1616,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)],[153]) ).
thf(643,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).
thf(2995,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)],[643]) ).
thf(420,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(2338,plain,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(854,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(3675,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)],[854]) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
thf(1732,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)],[192]) ).
thf(1118,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
thf(4572,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)],[1118]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( 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 ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(2909,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( 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 ) @ B ) ) )
& ( ( ( 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 ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(894,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(3807,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( hAPP @ ( hAPP @ ( 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)],[894]) ).
thf(344,axiom,
( ( c_RComplete_Onatfloor @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__zero) ).
thf(2144,plain,
( ( c_RComplete_Onatfloor @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
thf(1727,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ 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_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
thf(1251,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)],[26]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(4131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(539,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(2677,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(204,axiom,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(1754,plain,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1126,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/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(4594,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)],[1126]) ).
thf(916,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/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(3890,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)],[916]) ).
thf(788,axiom,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
thf(3491,plain,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(1113,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(4562,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(509,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(2602,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)],[509]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__le__cancel__iff) ).
thf(1278,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(257,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
thf(1906,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(848,axiom,
class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
thf(3660,plain,
class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
thf(2001,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)],[291]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
thf(2391,plain,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(615,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/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(2904,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)],[615]) ).
thf(179,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(1698,plain,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
thf(1959,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)],[273]) ).
thf(983,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(4116,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[983]) ).
thf(396,axiom,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(2275,plain,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(302,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(2033,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)],[302]) ).
thf(667,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/sandbox2/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
thf(3079,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)],[667]) ).
thf(1068,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(4412,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(2941,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(2028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(803,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
<=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
thf(3523,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(560,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
thf(2734,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(64,axiom,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(1374,plain,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1128,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero) ).
thf(4599,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(260,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
thf(1916,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(709,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(3234,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(252,axiom,
class_Rings_Osemiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(1884,plain,
class_Rings_Osemiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(801,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).
thf(3519,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(994,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(4159,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[994]) ).
thf(360,axiom,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
thf(2188,plain,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(2489,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(1188,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(4801,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
thf(3900,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(341,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/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(2134,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)],[341]) ).
thf(665,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
thf(3070,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_RComplete_Onatfloor @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
thf(2727,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_RComplete_Onatfloor @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_RComplete_Onatfloor @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(152,axiom,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1615,plain,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(72,axiom,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1389,plain,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).
thf(3255,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
& ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(167,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_RComplete_Onatfloor @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).
thf(1652,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_RComplete_Onatfloor @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(668,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/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(3081,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)],[668]) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(2016,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)],[295]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(2568,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
thf(1795,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)],[213]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).
thf(3590,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1044,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
thf(4328,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(121,axiom,
class_Rings_Olinordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1520,plain,
class_Rings_Olinordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(3868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[912]) ).
thf(364,axiom,
class_Rings_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(2193,plain,
class_Rings_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(1001,axiom,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
thf(4186,plain,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(1707,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)],[182]) ).
thf(677,axiom,
( ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ v_c____ )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
=> ? [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).
thf(3123,plain,
( ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ v_c____ )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
=> ? [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(3416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1030,axiom,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
thf(4273,plain,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(670,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/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(3091,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)],[670]) ).
thf(816,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(3568,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(161,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
thf(1638,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(688,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/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
thf(3170,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)],[688]) ).
thf(804,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/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(3532,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)],[804]) ).
thf(703,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(3223,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(4251,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1107,axiom,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
thf(4537,plain,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(890,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 @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(3796,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 @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(881,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(3751,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(374,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_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).
thf(2220,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_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(936,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Obounded) ).
thf(3964,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(1186,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(4796,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(610,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/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(2891,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)],[610]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(3726,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1371,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)],[63]) ).
thf(666,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(3077,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(1142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
thf(4645,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(860,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ ) )
=> ( ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) )
=> ? [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less_Ohyps) ).
thf(3695,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ ) )
=> ( ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) )
=> ? [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(978,axiom,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
thf(4099,plain,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[978]) ).
thf(996,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/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
thf(4171,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)],[996]) ).
thf(1014,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__inverse__lemma) ).
thf(4218,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1147,axiom,
~ ! [A: $i,B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096) ).
thf(4672,plain,
~ ! [A: $i,B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(646,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/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(3002,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)],[646]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
thf(1239,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)],[21]) ).
thf(288,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(1997,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(566,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/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
thf(2753,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)],[566]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(3436,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(457,axiom,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(2442,plain,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(567,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(2759,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(351,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
thf(2166,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)],[351]) ).
thf(820,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/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
thf(3579,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)],[820]) ).
thf(255,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/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
thf(1897,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)],[255]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(2557,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(427,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(2358,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(410,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(2319,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1074,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 ) ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(4433,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 ) ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(480,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/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(2510,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)],[480]) ).
thf(855,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(3678,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)],[855]) ).
thf(407,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/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(2311,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)],[407]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(3352,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(1159,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(4704,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[1159]) ).
thf(897,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(3815,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(449,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/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).
thf(2415,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)],[449]) ).
thf(218,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ouminus @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
thf(1806,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ouminus @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(798,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/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse) ).
thf(3515,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)],[798]) ).
thf(865,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).
thf(3710,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[865]) ).
thf(1178,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(4773,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(316,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
thf(2065,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(4228,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(947,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/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
thf(3996,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)],[947]) ).
thf(835,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(3631,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)],[835]) ).
thf(237,axiom,
class_Rings_Olinordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(1853,plain,
class_Rings_Olinordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
thf(1408,plain,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1094,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
thf(4498,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(469,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD) ).
thf(2478,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)],[469]) ).
thf(1055,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
thf(4369,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_RComplete_Onatfloor @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
thf(2422,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_RComplete_Onatfloor @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1035,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).
thf(4305,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)],[1035]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
thf(2906,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(3419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
thf(1349,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(326,axiom,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(2097,plain,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(721,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
thf(3270,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(874,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(3732,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)],[874]) ).
thf(399,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
thf(2284,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1129,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/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
thf(4601,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)],[1129]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(3468,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[779]) ).
thf(127,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
thf(1542,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(1722,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1190,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(4805,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
thf(4586,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(333,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(2116,plain,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1012,axiom,
! [A: $i,B: $i] :
( ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ A ) ) @ ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__real__of__nat__Suc__mult) ).
thf(4213,plain,
! [A: $i,B: $i] :
( ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ A ) ) @ ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(3197,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
thf(2856,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(2802,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[580]) ).
thf(681,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(3138,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(176,axiom,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(1690,plain,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(612,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).
thf(2896,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)],[612]) ).
thf(356,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
thf(2180,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(357,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Odvd @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
thf(2182,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Odvd @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1064,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
thf(4401,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(248,axiom,
class_Groups_Ouminus @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
thf(1877,plain,
class_Groups_Ouminus @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(2812,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[584]) ).
thf(563,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/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
thf(2742,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)],[563]) ).
thf(661,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
thf(3055,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[661]) ).
thf(1117,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(4569,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)],[1117]) ).
thf(329,axiom,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(2111,plain,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(4452,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1032,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/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
thf(4277,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)],[1032]) ).
thf(1010,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(4208,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ D @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(4332,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ D @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(775,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(3451,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).
thf(4652,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
<=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(4296,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(384,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2252,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(622,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(2928,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(637,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/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(2974,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)],[637]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( 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_Oorder @ C @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
thf(2842,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( 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_Oorder @ C @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(1070,axiom,
( v_a____
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I1_J) ).
thf(4420,plain,
( v_a____
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1079,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_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A )
& ! [D: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).
thf(4445,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_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A )
& ! [D: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(652,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(3027,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)],[652]) ).
thf(338,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
thf(2129,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(519,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).
thf(2625,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)],[519]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(1630,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(286,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
thf(1993,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)],[286]) ).
thf(573,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(2780,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(391,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(2267,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(387,axiom,
class_Rings_Odvd @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
thf(2261,plain,
class_Rings_Odvd @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1027,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(4264,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(448,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
thf(2410,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)],[448]) ).
thf(620,axiom,
! [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ A ) @ v_k____ ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_a____ @ v_s____ ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I4_J) ).
thf(2923,plain,
! [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ A ) @ v_k____ ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_a____ @ v_s____ ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(785,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/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
thf(3483,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)],[785]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).
thf(1344,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)],[53]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
thf(1556,plain,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(400,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
thf(2289,plain,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(783,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(3480,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(1,conjecture,
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ v_w____ ) )
= ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ v_a____ ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ v_k____ ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ v_w____ ) )
!= ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ v_a____ ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ v_k____ ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1198,plain,
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ v_w____ ) )
!= ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ v_a____ ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ v_k____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(1699,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)],[180]) ).
thf(674,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(3110,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)],[674]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
thf(4502,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(684,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(3159,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( hAPP @ ( 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)],[684]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(2931,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(712,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).
thf(3241,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)],[712]) ).
thf(297,axiom,
class_Fields_Ofield @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
thf(2022,plain,
class_Fields_Ofield @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(635,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
thf(2967,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(743,axiom,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_q____ )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lgqr) ).
thf(3348,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_q____ )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(1088,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
thf(4481,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
thf(1562,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(571,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/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(2770,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)],[571]) ).
thf(450,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(2418,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)],[450]) ).
thf(633,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(2962,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0) ).
thf(2365,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)],[430]) ).
thf(884,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/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(3759,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)],[884]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ C @ B @ A )
<=> ! [D: $i,E: $i] :
( ( hAPP @ A @ D )
= ( hAPP @ A @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_constant__def) ).
thf(2835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ C @ B @ A )
=> ! [D: $i,E: $i] :
( ( hAPP @ A @ D )
= ( hAPP @ A @ E ) ) )
& ( ! [D: $i,E: $i] :
( ( hAPP @ A @ D )
= ( hAPP @ A @ E ) )
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(311,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(2051,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)],[311]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
thf(1245,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)],[23]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(1445,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)],[95]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(2620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(565,axiom,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(2752,plain,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
thf(1435,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)],[91]) ).
thf(113,axiom,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(1496,plain,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel) ).
thf(4196,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(797,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/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
thf(3512,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)],[797]) ).
thf(691,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/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
thf(3178,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)],[691]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
thf(3908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(914,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(3876,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(380,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
thf(2239,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(535,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/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(2665,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)],[535]) ).
thf(1025,axiom,
class_Rings_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
thf(4260,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(575,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/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
thf(2784,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)],[575]) ).
thf(530,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(2652,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(3672,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(284,axiom,
class_Groups_Ozero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(1990,plain,
class_Groups_Ozero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(1340,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)],[51]) ).
thf(272,axiom,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(1958,plain,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ A @ D ) ) @ B )
=> ( c_SEQ_OBseq @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BseqI) ).
thf(2899,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ A @ D ) ) @ B )
=> ( c_SEQ_OBseq @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(1193,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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).
thf(4812,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)],[1193]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(4168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(906,axiom,
( v_k____
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I2_J) ).
thf(3849,plain,
( v_k____
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(156,axiom,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(1626,plain,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(649,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/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).
thf(3009,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)],[649]) ).
thf(1061,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(4394,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(513,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(2614,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)],[513]) ).
thf(765,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
thf(3427,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(4013,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(942,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(3981,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[942]) ).
thf(605,axiom,
class_Rings_Odvd @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
thf(2878,plain,
class_Rings_Odvd @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(30,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(1277,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1040,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
!= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
thf(4319,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
!= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(4177,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(521,axiom,
class_Rings_Ocomm__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
thf(2629,plain,
class_Rings_Ocomm__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( c_Polynomial_Osmult @ D @ B @ A ) )
= ( c_Polynomial_Osmult @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
thf(4688,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( c_Polynomial_Osmult @ D @ B @ A ) )
= ( c_Polynomial_Osmult @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(417,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/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
thf(2333,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)],[417]) ).
thf(593,axiom,
class_Groups_Oone @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
thf(2846,plain,
class_Groups_Oone @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(385,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 @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
thf(2256,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 @ A @ 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)],[385]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__mult) ).
thf(4113,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(481,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(2513,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)],[481]) ).
thf(214,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(1798,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)],[214]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(3376,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( A
= ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(552,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(2715,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)],[552]) ).
thf(959,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/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
thf(4035,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)],[959]) ).
thf(1091,axiom,
! [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_qr) ).
thf(4490,plain,
! [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(435,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/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(2375,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)],[435]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
thf(1225,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)],[14]) ).
thf(136,axiom,
! [A: $i] :
( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
thf(1566,plain,
! [A: $i] :
( ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(1647,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)],[165]) ).
thf(847,axiom,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
thf(3659,plain,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(559,axiom,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
thf(2732,plain,
! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(554,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/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
thf(2720,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)],[554]) ).
thf(609,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).
thf(2888,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)],[609]) ).
thf(607,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(2882,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(545,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(2689,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(4045,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1145,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
<=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ? [D: $i] :
! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( hAPP @ A @ E ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ D ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff2) ).
thf(4658,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ? [D: $i] :
! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( hAPP @ A @ E ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ D ) ) ) @ C ) ) )
& ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ? [D: $i] :
! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( hAPP @ A @ E ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ D ) ) ) @ C ) )
=> ( c_SEQ_OBseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
thf(1547,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_RComplete_Onatfloor @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).
thf(1748,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_RComplete_Onatfloor @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(599,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BseqD) ).
thf(2863,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(734,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__bound__exists) ).
thf(3315,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(144,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
thf(1598,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)],[144]) ).
thf(444,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/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
thf(2397,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)],[444]) ).
thf(795,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/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(3507,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)],[795]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).
thf(3754,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(717,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(3260,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[717]) ).
thf(505,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/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
thf(2588,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)],[505]) ).
thf(679,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/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
thf(3129,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)],[679]) ).
thf(932,axiom,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
thf(3949,plain,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(540,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
thf(2678,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)],[540]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( c_Rings_Odvd__class_Odvd @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
thf(2518,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)],[482]) ).
thf(61,axiom,
class_Rings_Oordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1368,plain,
class_Rings_Oordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(706,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(3228,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1084,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mrmq__eq) ).
thf(4469,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(587,axiom,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ v_c____ )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pqc0) ).
thf(2821,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ v_c____ )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(203,axiom,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(1753,plain,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(446,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
thf(2407,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(662,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(3058,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(123,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(1531,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(1042,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(4324,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[1042]) ).
thf(1137,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).
thf(4630,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ouminus @ B )
=> ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(1230,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ouminus @ B )
=> ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(595,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(2850,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(1484,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)],[110]) ).
thf(348,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
thf(2160,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(532,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).
thf(2656,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(1101,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(4522,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(840,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/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
thf(3642,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)],[840]) ).
thf(324,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
thf(2092,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(949,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/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(4003,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)],[949]) ).
thf(18,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
thf(1235,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)],[18]) ).
thf(419,axiom,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(2337,plain,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(831,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(3623,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)],[831]) ).
thf(738,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/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
thf(3329,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)],[738]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__inj__iff) ).
thf(1579,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(11,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1220,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(867,axiom,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(3715,plain,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(1067,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/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
thf(4409,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)],[1067]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(3246,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(1076,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(4437,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(185,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
thf(1716,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
thf(2224,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)],[376]) ).
thf(461,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
thf(2454,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( 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 )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(89,axiom,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1432,plain,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1003,axiom,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
thf(4190,plain,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(350,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(2165,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
thf(1452,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)],[99]) ).
thf(888,axiom,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less_Oprems) ).
thf(3791,plain,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel2) ).
thf(3202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__0 @ E )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
thf(4222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__0 @ E )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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)],[1016]) ).
thf(245,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(1869,plain,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(2276,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)],[397]) ).
thf(373,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2219,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(3774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(227,axiom,
class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
thf(1830,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
thf(3828,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
thf(2322,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)],[412]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(2701,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(493,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/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(2545,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)],[493]) ).
thf(33,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(1285,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(195,axiom,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
thf(1738,plain,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(1218,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(235,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
thf(1849,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)],[235]) ).
thf(331,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
thf(2113,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)],[331]) ).
thf(642,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
thf(2992,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)],[642]) ).
thf(216,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
thf(1802,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)],[216]) ).
thf(1136,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/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(4624,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)],[1136]) ).
thf(12,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1221,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(426,axiom,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
thf(2357,plain,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(411,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
thf(2320,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)],[411]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(2579,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(676,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
thf(3117,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)],[676]) ).
thf(627,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(2939,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1069,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
<=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(4414,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(538,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(2675,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)],[538]) ).
thf(77,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
thf(1404,plain,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
thf(1543,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)],[128]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1766,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)],[207]) ).
thf(1108,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(4538,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
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 @ C @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(1427,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)],[87]) ).
thf(1021,axiom,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_k____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096psize_Ap_A_061_Ak_A_L_A1_096) ).
thf(4235,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_k____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(140,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
thf(1585,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)],[140]) ).
thf(1155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(4695,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(651,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
thf(3024,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[651]) ).
thf(1028,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(4267,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(2030,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)],[301]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(4225,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1050,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(4342,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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)],[1050]) ).
thf(251,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/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(1881,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)],[251]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(2807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(29,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(1272,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(683,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).
thf(3156,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)],[683]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Obounded) ).
thf(3007,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(390,axiom,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(2266,plain,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1099,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(4516,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1060,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(4392,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(3288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(266,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/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
thf(1940,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)],[266]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(3433,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
thf(1839,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)],[231]) ).
thf(586,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).
thf(2818,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1177,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__inverse) ).
thf(4770,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(547,axiom,
( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).
thf(2696,plain,
( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
thf(1817,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)],[223]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(1913,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(773,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(3447,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(1182,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/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
thf(4780,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)],[1182]) ).
thf(73,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero__imp__ge__one) ).
thf(1390,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
thf(2226,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)],[377]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(4310,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(4730,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(456,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/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(2435,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)],[456]) ).
thf(1140,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/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(4639,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)],[1140]) ).
thf(568,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/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
thf(2760,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)],[568]) ).
thf(84,axiom,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(1421,plain,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(782,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/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(3478,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)],[782]) ).
thf(261,axiom,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
thf(1918,plain,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(3457,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( 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 ) @ B )
| ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( c_fequal @ B @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1649,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( c_fequal @ B @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1156,axiom,
( ( c_Complex_Ocis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__zero) ).
thf(4698,plain,
( ( c_Complex_Ocis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(424,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/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(2352,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)],[424]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ D )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).
thf(4727,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ D )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ B ) ) )
& ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ B ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(323,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
thf(2088,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)],[323]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1459,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)],[103]) ).
thf(308,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(2045,plain,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(268,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
thf(1949,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)],[268]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(2870,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ ( c_Complex_Ocis @ A ) )
= ( c_Complex_Ocis @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__mult) ).
thf(3188,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ ( c_Complex_Ocis @ A ) )
= ( c_Complex_Ocis @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(809,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(3548,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
thf(2194,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ 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_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(423,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(2347,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)],[423]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
thf(1412,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(413,axiom,
! [A: $i] :
( ( c_RComplete_Onatfloor @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
thf(2325,plain,
! [A: $i] :
( ( c_RComplete_Onatfloor @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(926,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/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
thf(3928,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)],[926]) ).
thf(644,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
thf(2997,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)],[644]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(4102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) )
& ( ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(289,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
thf(1998,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(824,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/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(3593,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)],[824]) ).
thf(458,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
thf(2443,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)],[458]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
thf(3613,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(189,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(1721,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(394,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(2273,plain,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
thf(2389,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)],[441]) ).
thf(327,axiom,
class_Groups_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2098,plain,
class_Groups_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(173,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1674,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(495,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(2554,plain,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(199,axiom,
class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
thf(1745,plain,
class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(792,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 ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(3501,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 ) @ ( hAPP @ ( hAPP @ ( 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)],[792]) ).
thf(1196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(4823,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1103,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(4527,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(873,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
thf(3729,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)],[873]) ).
thf(923,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
thf(3911,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(2853,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(401,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(2290,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(900,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/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
thf(3825,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)],[900]) ).
thf(487,axiom,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(2532,plain,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(4681,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
thf(1508,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)],[118]) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1481,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)],[109]) ).
thf(1151,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).
thf(4683,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)],[1151]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(2823,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(962,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
thf(4042,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)],[962]) ).
thf(1184,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(4791,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(292,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/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
thf(2004,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)],[292]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
thf(3748,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(299,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
thf(2026,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(834,axiom,
class_Rings_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
thf(3630,plain,
class_Rings_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).
thf(1854,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1048,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(4338,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(950,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(4010,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)],[950]) ).
thf(1093,axiom,
! [A: $i,B: $i] :
( ( ( class_RealVector_Oreal__normed__div__algebra @ B )
& ( class_Rings_Odivision__ring__inverse__zero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__inverse) ).
thf(4495,plain,
! [A: $i,B: $i] :
( ( ( class_RealVector_Oreal__normed__div__algebra @ B )
& ( class_Rings_Odivision__ring__inverse__zero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(625,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(2934,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(388,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(2262,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1026,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
thf(4261,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)],[1026]) ).
thf(443,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/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
thf(2394,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)],[443]) ).
thf(629,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
thf(2944,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)],[629]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
thf(1491,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)],[111]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ? [D: $i] :
! [E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ D @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ E ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ A @ C ) ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__infinity) ).
thf(3978,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ? [D: $i] :
! [E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ D @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ E ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ A @ C ) ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ C ) )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
thf(3324,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ C ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) )
& ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(917,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ A )
= ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DeMoivre) ).
thf(3896,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ A )
= ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(4478,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ 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 @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(429,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).
thf(2362,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)],[429]) ).
thf(148,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
thf(1607,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)],[148]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(3993,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(171,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(1661,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(972,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
thf(4074,plain,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1056,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(4372,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inverse) ).
thf(3552,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(2019,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)],[296]) ).
thf(151,axiom,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1614,plain,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2009,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)],[294]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
thf(1861,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(692,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
thf(3181,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(2384,plain,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(467,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
thf(2475,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)],[467]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).
thf(3585,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(3430,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1125,axiom,
! [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_c____ @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q_I2_J) ).
thf(4591,plain,
! [A: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ A )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_c____ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ ( c_Polynomial_Osmult @ D @ C @ B ) ) @ A )
= ( c_Polynomial_Osmult @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__left) ).
thf(3598,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ ( c_Polynomial_Osmult @ D @ C @ B ) ) @ A )
= ( c_Polynomial_Osmult @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(463,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
thf(2462,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)],[463]) ).
thf(93,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
thf(1440,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(415,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(2330,plain,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(889,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/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
thf(3793,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)],[889]) ).
thf(541,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/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(2680,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)],[541]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(1212,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)],[7]) ).
thf(303,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
thf(2036,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)],[303]) ).
thf(841,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).
thf(3645,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(475,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(2494,plain,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(1442,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(258,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
thf(1908,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(434,axiom,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(2374,plain,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(208,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
thf(1774,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)],[208]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( c_Rings_Odvd__class_Odvd @ C @ A @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).
thf(3705,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( c_Rings_Odvd__class_Odvd @ C @ A @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1192,axiom,
class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
thf(4811,plain,
class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(827,axiom,
? [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ? [C: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ C ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) )
& ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ D ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ B @ C ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096) ).
thf(3601,plain,
? [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ? [C: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ C ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) )
& ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ D ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ B @ C ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(129,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1546,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(802,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(3521,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1146,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/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
thf(4663,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)],[1146]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ~ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
thf(2768,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ~ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(4597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(3164,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(335,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__self) ).
thf(2123,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(986,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
thf(4125,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(386,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(2258,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)],[386]) ).
thf(138,axiom,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
thf(1578,plain,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1063,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(4399,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(910,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(3860,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B = A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(1678,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( B = A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(727,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
thf(3291,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1053,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(4356,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(1162,axiom,
( ( c_Complex_Oexpi @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expi__zero) ).
thf(4719,plain,
( ( c_Complex_Oexpi @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
thf(2522,plain,
! [A: $i,B: $i] :
( ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(3837,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ 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 @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(1380,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)],[69]) ).
thf(585,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(2815,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(41,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
thf(1303,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)],[41]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
thf(1986,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)],[282]) ).
thf(680,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
thf(3132,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)],[680]) ).
thf(24,axiom,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(1248,plain,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(310,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(2050,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1081,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
thf(4455,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3062,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(650,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(1859,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)],[240]) ).
thf(359,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
thf(2186,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)],[359]) ).
thf(1011,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(4210,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( 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)],[1011]) ).
thf(133,axiom,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
thf(1561,plain,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(1410,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)],[80]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(1288,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)],[35]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(3633,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(764,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/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
thf(3424,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)],[764]) ).
thf(659,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(3045,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)],[659]) ).
thf(893,axiom,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_qnc) ).
thf(3805,plain,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
thf(1742,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)],[198]) ).
thf(732,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
thf(3309,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(526,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/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(2636,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)],[526]) ).
thf(367,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2201,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(283,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(1989,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1173,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/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(4755,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)],[1173]) ).
thf(169,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
thf(1657,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1073,axiom,
~ ! [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ ) )
=> ~ ! [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_c____ @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(4427,plain,
~ ! [A: $i] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ A )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_pa____ ) )
=> ~ ! [B: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_pa____ ) @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ v_c____ @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1085,axiom,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
thf(4474,plain,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(49,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
thf(1335,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
thf(4024,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(318,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
thf(2070,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(868,axiom,
( ( c_Transcendental_Oln @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__one) ).
thf(3716,plain,
( ( c_Transcendental_Oln @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(653,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/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
thf(3030,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)],[653]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(4442,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(958,axiom,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
thf(4034,plain,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(885,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(3765,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( 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 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(54,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(1346,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)],[54]) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(2063,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)],[315]) ).
thf(150,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1610,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(3244,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[713]) ).
thf(465,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(2467,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
thf(1976,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)],[279]) ).
thf(755,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
thf(3392,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(491,axiom,
class_Power_Opower @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(2539,plain,
class_Power_Opower @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
thf(2687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(40,axiom,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1299,plain,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1051,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(4345,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)],[1051]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
thf(2138,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)],[343]) ).
thf(347,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(2159,plain,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
thf(3362,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(583,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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).
thf(2810,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)],[583]) ).
thf(939,axiom,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096) ).
thf(3974,plain,
~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(225,axiom,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(1827,plain,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(454,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2430,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)],[454]) ).
thf(862,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(3701,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(124,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
thf(1532,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)],[124]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(4799,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(2847,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(3570,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
<=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
thf(1537,plain,
! [A: $i,B: $i] :
( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A ) )
& ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A )
=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(3360,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(67,axiom,
class_Groups_Ouminus @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
thf(1378,plain,
class_Groups_Ouminus @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
thf(2583,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(969,axiom,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r01) ).
thf(4066,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1089,axiom,
! [A: $i] :
( ( c_Complex_Orcis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__zero__mod) ).
thf(4484,plain,
! [A: $i] :
( ( c_Complex_Orcis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(787,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(3489,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(898,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/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).
thf(3817,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)],[898]) ).
thf(115,axiom,
class_Rings_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1500,plain,
class_Rings_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1009,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(4206,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(1925,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)],[263]) ).
thf(971,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(4071,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)],[971]) ).
thf(675,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_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).
thf(3113,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_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(3394,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(2484,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(1885,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)],[253]) ).
thf(1154,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Odecseq @ B @ A )
<=> ! [C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) @ ( hAPP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__def) ).
thf(4691,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_SEQ_Odecseq @ B @ A )
=> ! [C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) @ ( hAPP @ A @ C ) ) ) )
& ( ! [C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) @ ( hAPP @ A @ C ) ) )
=> ( c_SEQ_Odecseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
thf(1505,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)],[117]) ).
thf(75,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(1399,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
thf(1621,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1105,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(4533,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(1047,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/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(4335,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)],[1047]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Rings_Odvd @ C )
& ( class_Rings_Osemiring__0 @ C ) )
=> ( ? [D: $i] : ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
thf(3950,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Rings_Odvd @ C )
& ( class_Rings_Osemiring__0 @ C ) )
=> ( ( ? [D: $i] : ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1031,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(4274,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(1962,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)],[274]) ).
thf(832,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(3626,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(135,axiom,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
thf(1565,plain,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(600,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/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
thf(2866,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)],[600]) ).
thf(1071,axiom,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_q____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096psize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_061_Apsize_Aq_096) ).
thf(4423,plain,
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ tc_Complex_Ocomplex @ v_q____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(354,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/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(2170,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)],[354]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(3035,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(355,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/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
thf(2177,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)],[355]) ).
thf(1144,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 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ A ) @ ( c_Polynomial_Opcompose @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
thf(4655,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 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ A ) @ ( c_Polynomial_Opcompose @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(2879,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1141,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(4642,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(705,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
thf(3227,plain,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1158,axiom,
( v_s____
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s0) ).
thf(4702,plain,
( v_s____
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(369,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(2206,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)],[369]) ).
thf(194,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(1737,plain,
class_Rings_Omult__zero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(4767,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[1176]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
thf(3405,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(234,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
thf(1848,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',fact_monom__Suc) ).
thf(2059,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)],[313]) ).
thf(1172,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(4752,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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)],[1172]) ).
thf(1038,axiom,
! [A: $i] :
( ( c_Complex_Ocis @ A )
= ( c_Complex_Orcis @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__rcis__eq) ).
thf(4313,plain,
! [A: $i] :
( ( c_Complex_Ocis @ A )
= ( c_Complex_Orcis @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(4056,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(660,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(3052,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)],[660]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(3637,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(699,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).
thf(3200,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(363,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
thf(2191,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)],[363]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
thf(1204,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)],[5]) ).
thf(97,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
thf(1449,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(220,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
thf(1812,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)],[220]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(3721,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(997,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(4174,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)],[997]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(1417,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)],[82]) ).
thf(246,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
thf(1870,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)],[246]) ).
thf(44457,plain,
$false,
inference(cvc4,[status(thm)],[2163,2630,1369,1633,3167,3397,3449,2331,1956,2199,1665,1501,4201,2452,4560,1879,1337,1718,2094,3944,2612,4094,1469,2295,2306,3345,2336,2131,2072,3661,4062,1995,2263,3798,1559,2876,1237,4183,2921,3698,1315,2787,2499,1982,2427,2480,1750,2210,2117,4339,4075,2622,2062,3040,3108,1305,3680,1200,3534,4714,2976,3230,3813,2495,1808,2659,3509,3285,2953,1401,1422,2947,2099,2282,1591,3498,2380,1971,4614,4747,4487,4234,1655,4739,1735,2316,1872,3616,3781,4564,2901,2844,1458,3276,1497,1705,4543,4633,4403,3439,2607,2686,4575,1310,3332,3367,3648,3365,2918,4110,1867,4220,2184,2627,2168,1919,2459,3414,1342,4294,3562,1640,4435,2042,1354,2146,1222,2360,1746,3236,2432,3249,4679,3088,1359,4198,4775,4386,3335,4047,3350,3545,2723,4142,2046,2491,2548,3947,4803,1601,3466,4030,4137,4607,1366,2067,1967,4322,3880,1518,4610,2531,2405,1228,1623,3938,1792,2039,2667,3495,4761,2708,3653,4778,2682,3542,1455,3204,3442,3263,4439,3976,2328,4524,2735,4563,2698,1298,2339,3689,3342,2269,2274,3485,2562,2488,3803,2126,3043,3855,2571,3713,2691,2169,4617,4194,1609,4270,1641,3231,3099,1800,4119,3517,3840,1379,4353,4788,2373,4622,2635,2929,3312,3657,1931,3734,2520,2730,2301,1815,1494,2989,1362,4793,3557,1778,2388,3866,2533,1232,3268,2007,2222,4578,4018,3724,2782,2893,3473,1864,4724,1828,2540,4686,2777,2073,2950,2237,2616,4396,1465,4329,3966,1714,3670,4733,2291,1383,4134,3357,2555,3300,3986,1377,1215,1447,3505,1433,1405,1943,4082,3389,2508,3537,1928,2618,2833,3739,2190,3421,4364,2424,2371,2979,4307,2137,4040,3756,3955,2799,4038,2639,2965,4519,1600,4707,3870,3588,4379,1697,1242,3559,4588,3906,1521,3492,2718,2205,4475,2982,2884,3435,4700,3097,4604,3857,3503,4216,3303,1691,1438,3852,3635,3186,3318,1470,1311,3037,1604,3899,3984,3265,2646,1783,2737,2496,2790,4059,1868,2382,3550,2000,1636,2705,4466,2601,2249,2596,4375,3610,2937,4499,4493,2132,3664,1238,3471,1387,1900,4016,2805,3742,4091,3989,4128,3239,1824,2150,3207,3682,4021,3282,1837,4140,3297,3578,1951,4327,2609,4187,1836,1210,2213,2313,1281,1573,2653,3958,2445,3191,2464,2873,1365,2670,3810,4585,2477,1968,2565,1296,3718,4776,1687,1457,2345,3926,1392,3667,2228,2112,1291,3931,3033,3408,1740,3445,4027,4316,1270,2377,1804,1425,3704,3518,3746,3650,2638,2268,4123,3968,4808,3831,2115,3482,1762,1534,1953,4108,1375,4544,1856,4636,1587,1878,3386,2726,2631,1719,2537,1755,3941,3060,3176,4817,4676,1329,2023,3846,4750,2080,4054,2038,2085,3573,1964,1659,3000,4582,4721,1739,1461,4425,2868,3596,2053,2240,1842,4406,4191,4513,1214,3194,3555,4457,1644,4814,2472,4180,3294,4736,4530,1419,2968,1249,4508,2598,3743,2581,4540,3628,3920,3162,1627,1776,1263,3656,2125,1588,2536,1297,3126,1451,2304,3354,4068,1831,2355,4244,4829,3819,4237,4231,1852,1429,2862,2766,3692,4152,1720,1979,3005,1333,4535,2926,1202,4765,3173,2748,1466,3639,1515,1895,2617,2662,2529,3147,3454,2634,3903,1991,1318,1814,3225,4567,2208,4081,2043,3279,3183,1712,1846,3999,1286,3321,2368,2408,2793,2189,1616,2995,2338,3675,1732,4572,2909,3807,2144,1727,1251,4131,2677,1754,4594,3890,3491,4562,2602,1278,1906,3660,2001,2391,2904,1698,1959,4116,2275,2033,3079,4412,2941,2028,3523,2734,1374,4599,1916,3234,1884,3519,4159,2188,2489,4801,3900,2134,3070,2727,1615,1389,3255,1652,3081,2016,2568,1795,3590,4328,1520,3868,2193,4186,1707,3123,3416,4273,3091,3568,1638,3170,3532,3223,4251,4537,3796,3751,2220,3964,4796,2891,3726,1371,3077,4645,3695,4099,4171,4218,4672,3002,1239,1997,2753,3436,2442,2759,2166,3579,1897,2557,2358,2319,4433,2510,3678,2311,3352,4704,3815,2415,1806,3515,3710,4773,2065,4228,3996,3631,1853,1408,4498,2478,4369,2422,4305,2906,3419,1349,2097,3270,3732,2284,4601,3468,1542,1722,4805,4586,2116,4213,3197,2856,2802,3138,1690,2896,2180,2182,4401,1877,2812,2742,3055,4569,2111,4452,4277,4208,4332,3451,4652,4296,2252,2928,2974,2842,4420,4445,3027,2129,2625,1630,1993,2780,2267,2261,4264,2410,2923,3483,1344,1556,2289,3480,1198,1699,3110,4502,3159,2931,3241,2022,2967,3348,4481,1562,2770,2418,2962,2365,3759,2835,2051,1245,1445,2620,2752,1435,1496,4196,3512,3178,3908,3876,2239,2665,4260,2784,2652,3672,1990,1340,1958,2899,4812,4168,3849,1626,3009,4394,2614,3427,4013,3981,2878,1277,4319,4177,2629,4688,2333,2846,2256,4113,2513,1798,3376,2715,4035,4490,2375,1225,1566,1647,3659,2732,2720,2888,2882,2689,4045,4658,1547,1748,2863,3315,1598,2397,3507,3754,3260,2588,3129,3949,2678,2518,1368,3228,4469,2821,1753,2407,3058,1531,4324,4630,1230,2850,1484,2160,2656,4522,3642,2092,4003,1235,2337,3623,3329,1579,1220,3715,4409,3246,4437,1716,2224,2454,1432,4190,2165,1452,3791,3202,4222,1869,2276,2219,3774,1830,3828,2322,2701,2545,1285,1738,1218,1849,2113,2992,1802,4624,1221,2357,2320,2579,3117,2939,4414,2675,1404,2247,1543,1766,4538,1427,4235,1585,4695,3024,4267,2030,4225,4342,1881,2807,1272,3156,3007,2266,4516,4392,3288,1940,3433,1839,2818,4770,2696,1817,1913,3447,4780,1390,2226,4310,4730,2435,4639,2760,1421,3478,1918,3457,1649,4698,2352,4727,2088,1459,2045,1949,2870,3188,3548,2194,2347,1412,2325,3928,2997,4102,1998,3593,2443,3613,1721,2273,2389,2098,1674,2554,1745,3501,4823,4527,3729,3911,2853,2290,3825,2532,4681,1508,1481,4683,2823,4042,4791,2004,3748,2026,3630,1854,4338,4010,4495,2934,2262,4261,2394,2944,1491,3978,3324,3896,4478,2362,1607,3993,1661,4074,4372,3552,2019,1614,2009,1861,3181,2384,2475,3585,3430,4591,3598,2462,1440,2330,3793,2680,1212,2036,3645,2494,1442,1908,2374,1774,3705,4811,3601,1546,3521,4663,2768,4597,3164,2123,4125,2258,1578,4399,3860,1678,3291,4356,4719,2522,3837,1380,2815,1303,1986,3132,1248,2050,4455,3062,3015,1859,2186,4210,1561,1410,1288,3633,3424,3045,3805,1742,3309,2636,2201,1989,4755,1657,4427,4474,1335,4024,2070,3716,3030,4442,4034,3765,1346,2063,1610,3244,2467,1976,3392,2539,2687,1299,4345,2138,2159,3362,2810,3974,1827,2430,3701,1532,4799,2847,3570,1537,3360,1378,2583,4066,4484,3489,3817,1500,4206,1925,4071,3113,3394,2484,1885,4691,1505,1399,1621,4533,4335,3950,4274,1962,3626,1565,2866,4423,2170,3035,2177,4655,2879,4642,3227,4702,2206,1737,4767,3405,1848,2059,4752,4313,4056,3052,3637,3200,2191,1204,1449,1812,3721,4174,1417,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW255+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n002.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 15:01:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.82/1.14 % [INFO] Parsing done (264ms).
% 1.82/1.15 % [INFO] Running in sequential loop mode.
% 2.53/1.36 % [INFO] eprover registered as external prover.
% 2.53/1.37 % [INFO] cvc4 registered as external prover.
% 2.53/1.37 % [INFO] Scanning for conjecture ...
% 3.05/1.52 % [INFO] Found a conjecture and 1263 axioms. Running axiom selection ...
% 4.02/1.72 % [INFO] Axiom selection finished. Selected 1195 axioms (removed 68 axioms).
% 5.30/2.08 % [INFO] Problem is first-order (TPTP FOF).
% 5.37/2.12 % [INFO] Type checking passed.
% 5.47/2.12 % [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 ...
% 99.59/23.53 % External prover 'cvc4' found a proof!
% 99.59/23.53 % [INFO] Killing All external provers ...
% 99.59/23.54 % Time passed: 23000ms (effective reasoning time: 22386ms)
% 99.59/23.54 % 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)>
% 99.59/23.54 % Axioms used in derivation (1195): fact_dvd_Oord__less__eq__trans, fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096, fact_le__SucI, fact_smult__minus__left, fact_real__le__refl, arity_fun__Orderings_Oorder, fact_reals__Archimedean, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_dvd_Oless__trans, fact_minus__mult__left, fact_neg__le__0__iff__le, arity_Complex__Ocomplex__Rings_Odvd, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_one__dvd, fact_minus__monom, fact_xt1_I1_J, 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_real__less__def, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096, fact_power__strict__decreasing, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_kas_I4_J, fact_natfloor__real__of__nat, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_mult__poly__0__right, fact_nonzero__inverse__inverse__eq, fact_add__strict__right__mono, fact_incr__mult__lemma, fact_natfloor__power, fact_natfloor__add, fact_mult__1__left, fact_diff__0__eq__0, fact_zle__refl, fact_cis__inverse, fact_inverse__1, fact_dvd__mult__cancel__left, fact_zdvd__not__zless, fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_diff__add__inverse, fact_dvdI, fact_le__eq__less__or__eq, fact_minus__mult__right, fact_xt1_I4_J, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_q__pos__lemma, fact_add__poly__code_I2_J, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_order, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_mult__nonpos__nonpos, fact_dvd_Oeq__iff, fact_less__imp__inverse__less, fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096, fact_neg__equal__0__iff__equal, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_power__power__power, fact_real__of__nat__zero, fact_mult__left_Ominus, fact__096psize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_061_Apsize_Aq_096, fact_Bseq__iff3, fact_zdvd__antisym__nonneg, fact_power__inject__base, fact_norm__power, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_one__is__add, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_termination__basic__simps_I5_J, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, fact_norm__mult__less, fact_odd__nonzero, fact_mult_Opos__bounded, fact_dvd_Oorder__trans, fact_zminus__zminus, fact_mult__nonneg__nonpos, fact_poly__eq__0__iff__dvd, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_split__mult__neg__le, fact_inverse__inverse__eq, fact_unity__coeff__ex, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_poly__bound__exists, fact_add__less__mono, fact_mult__pCons__right, fact_real__0__less__add__iff, fact_mult__eq__0__iff, fact_pow__divides__pow__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_smult__dvd__cancel, arity_Nat__Onat__Orderings_Oorder, 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_n__less__m__mult__n, fact_ln__eq__zero__iff, fact_ln__inj__iff, fact_Suc__mono, fact_inverse__add, fact_zero__less__power, 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, fact_one__less__inverse__iff, arity_RealDef__Oreal__Rings_Osemiring__0, arity_RealDef__Oreal__Rings_Olinordered__ring, fact_mult__le__less__imp__less, fact_zadd__commute, fact_BseqD, fact_natceiling__le, fact_ln__less__cancel__iff, arity_Nat__Onat__Groups_Omonoid__mult, fact_power__increasing, fact_real__add__le__0__iff, fact_mult__0, fact_inverse__zero__imp__zero, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_zero__le__natfloor, fact_add__right__imp__eq, fact_nonzero__inverse__eq__imp__eq, fact_BseqI, fact_mult__mono, fact_gr0__conv__Suc, fact_less_Oprems, fact_zdvd__mult__cancel, fact_field__power__not__zero, fact_natceiling__le__eq__one, arity_RealDef__Oreal__Rings_Oidom, fact_Suc__le__mono, fact_dvd__smult, fact_mult__poly__0__left, fact_dvd_Oless__imp__not__less, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, fact_kas_I2_J, fact_pc0, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_mult_Ononneg__bounded, fact_nat__add__right__cancel, fact_neg__le__iff__le, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_inverse__zero, fact_dvd_Oord__eq__less__trans, fact_cq0, fact_mult__le__mono2, fact_le__neq__implies__less, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_smult__smult, fact_zle__linear, fact_zero__le__one, arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, fact_poly__add, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_cis__zero, fact_nat__add__left__cancel__less, fact_le__minus__iff, fact_mult__left_Ononneg__bounded, 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_q_I2_J, fact_mult__left__le__imp__le, fact_minus__add__cancel, fact_add__pos__nonneg, fact_dvd__diffD, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_pow__divides__pow__nat, fact_lemma__NBseq__def2, fact_order__1, fact_int__0__less__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_add__strict__increasing2, fact_order__less__imp__not__eq, 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, arity_Polynomial__Opoly__Rings_Olinordered__semidom, fact_smult__1__left, fact_mult__strict__left__mono, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, fact_add__nonneg__eq__0__iff, fact_real__mult__commute, 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_zadd__left__mono, fact_sum__squares__le__zero__iff, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_sum__squares__ge__zero, fact_add__increasing2, fact_pow__divides__eq__nat, arity_RealDef__Oreal__Fields_Ofield__inverse__zero, fact_dvd__reduce, fact_zero__le__mult__iff, arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, fact_natceiling__mono, fact_kas_I3_J, fact_synthetic__div__0, arity_Int__Oint__Groups_Ozero, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_mult_Ozero__left, fact_dvd__power__le, fact_real__of__nat__zero__iff, fact_poly__0, fact_add__mono, fact_gr0I, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, arity_Int__Oint__Rings_Olinordered__ring, fact_add__0__iff, fact_poly__smult, fact_add__right__mono, fact_minus__add, fact_reals__Archimedean4, fact_lemma__NBseq__def, fact_nat__less__real__le, fact_real__of__nat__less__iff, fact_one__less__power, fact_power__strict__increasing, fact_kas_I1_J, arity_Nat__Onat__Rings_Osemiring__0, fact_one__le__power, fact_even__less__0__iff, fact_self__quotient__aux1, fact_power__commutes, fact_power__real__of__nat, fact_le__natfloor__eq__one, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef__Oreal__Groups_Omonoid__mult, fact_add__monom, fact_add__0__left, arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, fact_power__minus, arity_Int__Oint__Groups_Ocancel__comm__monoid__add, fact_a00, fact_nat__dvd__not__less, fact_real__mult__assoc, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, fact_mult__eq__1__iff, fact_smult__add__right, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_power__eq__0__iff, 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arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_zdiv__mono2__neg__lemma, fact_ln__one, fact_natfloor__mono, fact_ln__ge__zero__iff, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 99.59/23.54 % No. of inferences in proof: 2394
% 99.59/23.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23000 ms resp. 22386 ms w/o parsing
% 100.67/23.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 100.67/23.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------